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  • On geometric quantization of $$b^m$$ b m -symplectic manifolds
    Math. Z. (IF 0.881) Pub Date : 2020-08-25
    Victor W. Guillemin, Eva Miranda, Jonathan Weitsman

    We study the formal geometric quantization of \(b^m\)-symplectic manifolds equipped with Hamiltonian actions of a torus T with nonzero leading modular weight. The resulting virtual \(T-\)modules are finite dimensional when m is odd, as in [4]; when m is even, these virtual modules are not finite dimensional, and we compute the asymptotics of the representations for large weight.

    更新日期:2020-08-25
  • Teichmüller spaces and Torelli theorems for hyperkähler manifolds
    Math. Z. (IF 0.881) Pub Date : 2020-08-20
    Eduard Looijenga

    Kreck and Yang Su recently gave counterexamples to a version of the Torelli theorem for hyperkählerian manifolds as stated by Verbitsky. We extract the correct statement and give a short proof of it. We also revisit a few of its consequences, some of which are given new (shorter) proofs, and ask some questions.

    更新日期:2020-08-20
  • Energy distribution of harmonic 1-forms and Jacobians of Riemann surfaces with a short closed geodesic
    Math. Z. (IF 0.881) Pub Date : 2020-08-17
    Peter Buser, Eran Makover, Bjoern Muetzel, Robert Silhol

    We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian variety of S develops into a variety that splits. If the geodesic is nonseparating then the Jacobian degenerates. The aim of this work is to get insight into this process and give estimates in

    更新日期:2020-08-18
  • Tian’s $$\alpha _{m,k}^{{\hat{K}}}$$ α m , k K ^ -invariants on group compactifications
    Math. Z. (IF 0.881) Pub Date : 2020-08-17
    Yan Li, Xiaohua Zhu

    In this paper, we compute Tian’s \(\alpha _{m,k}^{K\times K}\)-invariant on a polarized G-group compactification, where K denotes a maximal compact subgroup of a connected complex reductive group G. We prove that Tian’s conjecture (see Conjecture 1.1 below) is true for \(\alpha _{m,k}^{K\times K}\)-invariant on such manifolds when \(k=1\), but it fails in general by producing counter-examples when

    更新日期:2020-08-17
  • On the Geometric Subgroups of the Étale Fundamental Groups of Varieties over Real Closed Fields
    Math. Z. (IF 0.881) Pub Date : 2020-08-12
    Yuichiro Hoshi, Takahiro Murotani, Shota Tsujimura

    In the present paper, we establish a “group-theoretic” algorithm for reconstructing, from the étale fundamental group of a suitable proper normal variety over a real closed field, the geometric subgroup of the étale fundamental group of the proper normal variety.

    更新日期:2020-08-12
  • Cluster algebras arising from cluster tubes I: integer vectors
    Math. Z. (IF 0.881) Pub Date : 2020-08-12
    Changjian Fu, Shengfei Geng, Pin Liu

    We study cluster algebras arising from cluster tubes. We obtain categorical interpretations for g-vectors, c-vectors and denominator vectors for cluster algebras of type \(\mathrm {C}\) with respect to arbitrary initial seeds. In particular, a denominator theorem has been proved, which enables us to establish the linearly independence of denominator vectors of cluster variables from the same cluster

    更新日期:2020-08-12
  • A dynamical dimension transference principle for dynamical diophantine approximation
    Math. Z. (IF 0.881) Pub Date : 2020-08-11
    Bao-Wei Wang, Guo-Hua Zhang

    Diophantine approximation in dynamical systems concerns the Diophantine properties of the orbits. In classic Diophantine approximation, the powerful mass transference principle established by Beresnevich and Velani provides a general principle to the dimension for a limsup set. In this paper, we aim at finding a general principle for the dimension of the limsup set arising in a general expanding dynamical

    更新日期:2020-08-11
  • Structure constants for Chern classes of Schubert cells
    Math. Z. (IF 0.881) Pub Date : 2020-08-11
    Changjian Su

    A formula for the structure constants of the multiplication of Schubert classes is obtained in (Rebecca and Allen. arXiv preprint arXiv:1909.05283, 2019). In this note, we prove analogous formulae for the Chern–Schwartz–MacPherson (CSM) classes and Segre–Schwartz–MacPherson (SSM) classes of Schubert cells in the flag variety. By the equivalence between the CSM classes and the stable basis elements

    更新日期:2020-08-11
  • An algebraic model for rational naïve-commutative ring SO (2)-spectra and equivariant elliptic cohomology
    Math. Z. (IF 0.881) Pub Date : 2020-08-10
    David Barnes, J. P. C. Greenlees, Magdalena Kędziorek

    Equipping a non-equivariant topological \(\text {E}_\infty \)-operad with the trivial G-action gives an operad in G-spaces. For a G-spectrum, being an algebra over this operad does not provide any multiplicative norm maps on homotopy groups. Algebras over this operad are called naïve-commutative ring G-spectra. In this paper we take \(G=SO(2)\) and we show that commutative algebras in the algebraic

    更新日期:2020-08-10
  • Motivic Tambara functors
    Math. Z. (IF 0.881) Pub Date : 2020-08-09
    Tom Bachmann

    Let k be a field and denote by \(\mathcal {SH}(k)\) the motivic stable homotopy category. Recall its full subcategory \(\mathcal {SH}(k)^{{\text {eff}}\heartsuit }\) (Bachmann in J Topol 10(4):1124–1144. arXiv:1610.01346, 2017). Write \(\mathrm {NAlg}(\mathcal {SH}(k))\) for the category of \({\mathrm {S}\mathrm {m}}\)-normed spectra (Bachmann-Hoyois in arXiv:1711.03061, 2017); recall that there is

    更新日期:2020-08-10
  • Exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds
    Math. Z. (IF 0.881) Pub Date : 2020-08-09
    Werner Müller, Frédéric Rochon

    For \(d=2n+1\) a positive odd integer, we consider sequences of arithmetic subgroups of \({\text {SO}}_0(d,1)\) and yielding corresponding hyperbolic manifolds of finite volume and show that, under appropriate and natural assumptions, the torsion of the associated cohomology groups grows exponentially.

    更新日期:2020-08-10
  • On the modularity of 2-adic potentially semi-stable deformation rings
    Math. Z. (IF 0.881) Pub Date : 2020-08-09
    Shen-Ning Tung

    Using p-adic local Langlands correspondence for \({\text {GL}}_2(\mathbb {Q}_2)\) and an ordinary \(R = \mathbb {T}\) theorem, we prove that the support of patched modules for quaternionic forms meet every irreducible component of the potentially semi-stable deformation ring. This gives a new proof of the Breuil–Mézard conjecture for 2-dimensional representations of the absolute Galois group of \(\mathbb

    更新日期:2020-08-10
  • Metrisability of projective surfaces and pseudo-holomorphic curves
    Math. Z. (IF 0.881) Pub Date : 2020-08-08
    Thomas Mettler

    We show that the metrisability of an oriented projective surface is equivalent to the existence of pseudo-holomorphic curves. A projective structure \({\mathfrak {p}}\) and a volume form \(\sigma \) on an oriented surface M equip the total space of a certain disk bundle \(Z\rightarrow M\) with a pair \((J_{{\mathfrak {p}}},{\mathfrak {J}}_{{\mathfrak {p}},\sigma })\) of almost complex structures. A

    更新日期:2020-08-09
  • Tower power for S -adics
    Math. Z. (IF 0.881) Pub Date : 2020-08-08
    Nicolas Bédaride, Arnaud Hilion, Martin Lustig

    We explain and restate the results from our recent paper [2] in standard language for substitutions and S-adic systems in symbolic dynamics. We then produce as rather direct application an S-adic system (with finite set of substitutions S on d letters) that is minimal and has d distinct ergodic probability measures. As second application we exhibit a formula that allows an efficient practical computation

    更新日期:2020-08-09
  • Gelfand-type theorems for dynamical Banach modules
    Math. Z. (IF 0.881) Pub Date : 2020-08-08
    Henrik Kreidler, Sita Siewert

    The representation theorems of Gelfand and Kakutani for commutative C*-algebras and AM- and AL-spaces are the basis for the Koopman linearization of topological and measure-preserving dynamical systems. In this article we prove versions of these results for dynamics on topological and measurable Banach bundles and the corresponding weighted Koopman representations on Banach modules.

    更新日期:2020-08-08
  • Birational sheets in reductive groups
    Math. Z. (IF 0.881) Pub Date : 2020-08-07
    Filippo Ambrosio

    We define the group analogue of birational sheets, a construction performed by Losev for reductive Lie algebras. For G semisimple simply connected, we describe birational sheets in terms of Lusztig–Spaltenstein induction and we prove that they form a partition of G, and that they are unibranch varieties with smooth normalization by means of a local study.

    更新日期:2020-08-08
  • Infinitesimally tight Lagrangian orbits
    Math. Z. (IF 0.881) Pub Date : 2020-08-07
    Elizabeth Gasparim, Luiz A. B. San Martin, Fabricio Valencia

    We describe isotropic orbits for the restricted action of a subgroup of a Lie group acting on a symplectic manifold by Hamiltonian symplectomorphisms and admitting an Ad*-equivariant moment map. We obtain examples of Lagrangian orbits of complex flag manifolds, of cotangent bundles of orthogonal Lie groups, and of products of flags. We introduce the notion of infinitesimally tight and study the intersection

    更新日期:2020-08-08
  • Some remarks on Hermitian manifolds satisfying Kähler-like conditions
    Math. Z. (IF 0.881) Pub Date : 2020-08-07
    Anna Fino, Nicoletta Tardini

    We study Hermitian metrics whose Bismut connection \(\nabla ^B\) satisfies the first Bianchi identity in relation to the SKT condition and the parallelism of the torsion of the Bimut connection. We obtain a characterization of complex surfaces admitting Hermitian metrics whose Bismut connection satisfy the first Bianchi identity and the condition \(R^B(x,y,z,w)=R^B(Jx,Jy,z,w)\), for every tangent vectors

    更新日期:2020-08-08
  • Local-global principles for norm one tori over semi-global fields
    Math. Z. (IF 0.881) Pub Date : 2020-08-06
    Sumit Chandra Mishra

    Let K be a complete discretely valued field with the residue field \(\kappa \). Let F be the function field of a smooth, projective, geometrically integral curve over K and \(\mathscr {X}\) be a regular proper model of F such that the reduced special fibre X is a union of regular curves with normal crossings. Suppose that the graph associated to \(\mathscr {X}\) is a tree (e.g. \(F = K(t)\)). Let L/F

    更新日期:2020-08-06
  • Tropical theta functions and Riemann–Roch inequality for tropical Abelian surfaces
    Math. Z. (IF 0.881) Pub Date : 2020-08-04
    Ken Sumi

    We show that the space of theta functions on tropical tori is identified with a convex polyhedron. We also show a Riemann-Roch inequality for tropical abelian surfaces by calculating the self-intersection numbers of divisors.

    更新日期:2020-08-04
  • Serre–Tate theory for Shimura varieties of Hodge type
    Math. Z. (IF 0.881) Pub Date : 2020-07-15
    Ananth N. Shankar, Rong Zhou

    We study the formal neighbourhood of a point in the \(\mu \)-ordinary locus of an integral model of a Hodge type Shimura variety. We show that this formal neighbourhood has a structure of a “shifted cascade”. Moreover we show that the CM points on the formal neighbourhood are dense and that the identity section of the shifted cascade corresponds to a lift of the abelian variety which has a characterization

    更新日期:2020-07-15
  • An energy gap phenomenon for the Whitney sphere
    Math. Z. (IF 0.881) Pub Date : 2020-07-15
    Liuyang Zhang

    In this paper, we study Lagrangian surfaces satisfying \(\nabla ^*T=0\) , where \(T=-2\nabla ^*(\check{A}\lrcorner \omega )\) and \(\check{A}\) is the Lagrangian trace-free second fundamental form. We obtain a gap lemma for such a Lagrangian surface.

    更新日期:2020-07-15
  • t-Stabilities for a weighted projective line
    Math. Z. (IF 0.881) Pub Date : 2020-07-13
    Shiquan Ruan, Xintian Wang

    The present paper focuses on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the finest t-stabilities on certain triangulated category and, describe the semistable subcategories and last HN-triangles for coherent sheaves in \(D^b(\mathrm{coh\,}{{\mathbb {X}}})\), which is the bounded derived category of coherent

    更新日期:2020-07-13
  • Mixed norm Strichartz-type estimates for hypersurfaces in three dimensions
    Math. Z. (IF 0.881) Pub Date : 2020-07-12
    Ljudevit Palle

    In their work Ikromov and Müller (Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra. Princeton University Press, Princeton, 2016) proved the full range \(L^p-L^2\) Fourier restriction estimates for a very general class of hypersurfaces in \({\mathbb {R}}^3\) which includes the class of real analytic hypersurfaces. In this article we partly extend their results to the mixed

    更新日期:2020-07-13
  • Rigidity theorems for special Lagrangian cones
    Math. Z. (IF 0.881) Pub Date : 2020-07-11
    Caiyan Li

    In this paper, we derive that every n-dimensional (\(2\le n\le 7\)) special Lagrangian cones in \({\mathbb {R}}^{n}\times {\mathbb {R}}^{n}\) with flat normal bundle must be flat. And we also derive a rigidity result under a certain restriction on Gauss map.

    更新日期:2020-07-13
  • Theta lifts for Lorentzian lattices and coefficients of mock theta functions
    Math. Z. (IF 0.881) Pub Date : 2020-07-09
    Jan Hendrik Bruinier, Markus Schwagenscheidt

    We evaluate regularized theta lifts for Lorentzian lattices in three different ways. In particular, we obtain formulas for their values at special points involving coefficients of mock theta functions. By comparing the different evaluations, we derive recurrences for the coefficients of mock theta functions, such as Hurwitz class numbers, Andrews’ spt-function, and Ramanujan’s mock theta functions

    更新日期:2020-07-09
  • Generic representations of metaplectic groups and their theta lifts
    Math. Z. (IF 0.881) Pub Date : 2020-07-08
    Petar Bakić, Marcela Hanzer

    In this paper we give the description of generic representations of metaplectic groups over p-adic fields in terms of their Langlands parameters and calculate their theta lifts on all levels for any tower of odd orthogonal groups. We also describe precisely all the occurrences of the failure of the standard module conjecture for metaplectic groups.

    更新日期:2020-07-08
  • A liouville theorem on the PDE $$\det (f_{i\bar{\jmath }})=1$$ det ( f i ȷ ¯ ) = 1
    Math. Z. (IF 0.881) Pub Date : 2020-07-08
    An-Min Li, Li Sheng

    Let f be a smooth plurisubharmonic function which solves $$\begin{aligned} \det (f_{i\bar{\jmath }})=1\;\;\;\;\;\;\text{ on } \;\;\;\mathbb C^n. \end{aligned}$$ Suppose that the metric \(\omega _{f}=\sqrt{-1}f_{i\bar{\jmath }}dz_{i}\wedge d\bar{z}_{j}\) is complete and f satisfies the growth condition $$\begin{aligned} \mathsf N_{0}^{-1}(1+|z|^2)\le f\le \mathsf N_{0}(1+ |z|^2),\;\;\;\; \text{ as }\;\;\;

    更新日期:2020-07-08
  • Arithmetic of p -adic curves and sections of geometrically abelian fundamental groups
    Math. Z. (IF 0.881) Pub Date : 2020-07-04
    Mohamed Saïdi

    Let X be a proper, smooth, and geometrically connected curve of genus \(g(X)\ge 1\) over a p-adic local field. We prove that there exists an effectively computable open affine subscheme \(U\subset X\) with the property that \({\text {period}}(X)=1\), and \({\text {index}}(X)\) equals 1 or 2 (resp. \({\text {period}}(X)={\text {index}}(X)=1\), assuming \({\text {period}}(X)={\text {index}}(X)\)), if

    更新日期:2020-07-05
  • Twisted Fourier–Mukai partners of Enriques surfaces
    Math. Z. (IF 0.881) Pub Date : 2020-07-04
    Nicolas Addington, Andrew Wray

    Bridgeland and Maciocia showed that a complex Enriques surface X has no Fourier–Mukai partners apart from itself: that is, if \(D^b(X) \cong D^b(Y)\) then \(X \cong Y\). We extend this to twisted Fourier–Mukai partners: if \(\alpha \) is the non-trivial element of \({{\,\mathrm{Br}\,}}(X) = {\mathbb {Z}}/2\) and \(D^b(X,\alpha ) \cong D^b(Y,\beta )\), then \(X \cong Y\) and \(\beta \) is non-trivial

    更新日期:2020-07-05
  • Multiplicity one theorem for $$(\mathrm {GL}_{n+1},\mathrm {GL}_n)$$ ( GL n + 1 , GL n ) over a local field of positive characteristic
    Math. Z. (IF 0.881) Pub Date : 2020-07-03
    Dor Mezer

    Let \({\mathbb {F}}\) be a non-archimedean local field of characteristic different from 2. We consider distributions on \(\mathrm {GL}(n+1,{\mathbb {F}})\) which are invariant under the adjoint action of \(\mathrm {GL}(n,{\mathbb {F}})\). We prove that any such distribution is invariant under transposition. This implies that the restriction to \(\mathrm {GL}(n,{{\mathbb {F}}})\) of any irreducible

    更新日期:2020-07-03
  • KAM theory for the reversible perturbations of 2D linear beam equations
    Math. Z. (IF 0.881) Pub Date : 2020-07-03
    Chuanfang Ge, Jiansheng Geng, Zhaowei Lou

    In the present paper, we prove an infinite dimensional reversible Kolmogorov-Arnold-Moser (KAM) theorem. As an application, we study the existence of KAM tori for a class of two dimensional (2D) non-Hamiltonian completely resonant beam equations with derivative nonlinearities. The Birkhoff normal form theory is also used since there are no external parameters in the equations.

    更新日期:2020-07-03
  • Approximation in weighted Bergman spaces and Hankel operators on strongly pseudoconvex domains
    Math. Z. (IF 0.881) Pub Date : 2020-07-03
    Jinshou Gao, Zhangjian Hu

    Suppose D is a bounded strongly pseudoconvex domain in \({{\mathbb {C}}}^n\) with smooth boundary, and let \(\rho \) be its defining function. For \(1< p<\infty \) and \(\alpha >-1\), we show that the weighted Bergman projection \(P_\alpha \) is bounded on \(L^p(D, |\rho |^\alpha dV)\). With non-isotropic estimates for \(\overline{\partial }\) and Stein’s theorem on non-tangential maximal operators

    更新日期:2020-07-03
  • Waring–Goldbach problem involving cubes of primes
    Math. Z. (IF 0.881) Pub Date : 2020-07-03
    Tak Wing Ching, Kai Man Tsang

    It is widely conjectured that every sufficiently large integer satisfying certain necessary congruence conditions is the sum of 4 cubes of prime numbers. As an approximation to this conjecture, we shall establish two results in this paper. Firstly, we show that every large odd integer is the sum of a prime, 4 cubes of primes and 15 powers of 2. Secondly, we show that the conjecture is true for at least

    更新日期:2020-07-03
  • Extrinsic conformal lower bounds of eigenvalue for Dirac operator
    Math. Z. (IF 0.881) Pub Date : 2020-07-02
    Qun Chen, Linlin Sun

    In this note, we prove conformal lower bounds for Dirac operators of submanifolds in terms of conformal and extrinsic quantities.

    更新日期:2020-07-02
  • Hochschild cohomology and group actions
    Math. Z. (IF 0.881) Pub Date : 2020-07-02
    Alexander Perry

    Given a finite group action on a (suitably enhanced) triangulated category linear over a field, we establish a formula for the Hochschild cohomology of the category of invariants, assuming the order of the group is coprime to the characteristic of the base field. The formula shows that the cohomology splits canonically with one summand given by the invariant subspace of the Hochschild cohomology of

    更新日期:2020-07-02
  • A higher-order tangent map and a conjecture on the higher Nash blowup of curves
    Math. Z. (IF 0.881) Pub Date : 2020-07-02
    Enrique Chávez-Martínez, Daniel Duarte, Arturo Giles Flores

    We introduce a higher-order version of the tangent map of a morphism and find a matrix representation. We then apply this matrix to solve a conjecture by Yasuda regarding the semigroup of the higher Nash blowup of formal curves. We first show that the conjecture is true for toric curves. We conclude by exhibiting a family of non-monomial curves where the conjecture fails.

    更新日期:2020-07-02
  • Convergence of measures on compactifications of locally symmetric spaces
    Math. Z. (IF 0.881) Pub Date : 2020-07-01
    Christopher Daw, Alexander Gorodnik, Emmanuel Ullmo

    We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space \(S=\Gamma \backslash G/K\) is compact. More precisely, given a sequence of homogeneous probability measures on S, we expect that any weak limit is homogeneous with support contained in precisely one of the boundary components (including S itself). We introduce

    更新日期:2020-07-01
  • Measures of maximal entropy for suspension flows
    Math. Z. (IF 0.881) Pub Date : 2020-07-01
    Godofredo Iommi, Anibal Velozo

    We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any suspension flow defined over a sub-shift of finite type can be perturbed (by an arbitrarily small perturbation) so that the resulting flow has uncountably many ergodic

    更新日期:2020-07-01
  • A sharp exponent on sum of distance sets over finite fields
    Math. Z. (IF 0.881) Pub Date : 2020-07-01
    Doowon Koh, Thang Pham, Chun-Yen Shen, Le Anh Vinh

    We study a variant of the Erdős–Falconer distance problem in the setting of finite fields. More precisely, let E and F be sets in \(\mathbb {F}_q^d\), and \(\Delta (E), \Delta (F)\) be corresponding distance sets. We prove that if \(|E||F|\ge Cq^{d+\frac{1}{3}}\) for a sufficiently large constant C, then the set \(\Delta (E)+\Delta (F)\) covers at least a half of all distances. Our result in odd dimensional

    更新日期:2020-07-01
  • The Steinberg quotient of a tilting character
    Math. Z. (IF 0.881) Pub Date : 2020-07-01
    Paul Sobaje

    Let G be a simple algebraic group over an algebraically closed field of prime characteristic. If M is a finite dimensional G-module that is projective over the Frobenius kernel of G, then its character is divisible by the character of the Steinberg module. In this paper we study such quotients, showing that if M is an indecomposable tilting module, then the multiplicities of the orbit sums appearing

    更新日期:2020-07-01
  • Pseudo solutions, rotation sets, and shadowing rotations for monotone recurrence relations
    Math. Z. (IF 0.881) Pub Date : 2020-07-01
    Tong Zhou, Wen-Xin Qin

    By introducing for monotone recurrence relations pseudo solutions, which are analogues of pseudo orbits of dynamical systems, we show that for general monotone recurrence relations the rotation set is closed, and each element in the rotation set is realized by a Birkhoff orbit. Moreover, if there is an orbit without rotation number, then the system has positive topological entropy, and we can construct

    更新日期:2020-07-01
  • Bergman kernel and oscillation theory of plurisubharmonic functions
    Math. Z. (IF 0.881) Pub Date : 2020-06-30
    Bo-Yong Chen, Xu Wang

    Based on Harnack’s inequality and convex analysis we show that each plurisubharmonic function is locally BUO (bounded upper oscillation) with respect to polydiscs of finite type but not for arbitrary polydiscs. We also show that each function in the Lelong class is globally BUO with respect to all polydiscs. A dimension-free BUO estimate is obtained for the logarithm of the modulus of a complex polynomial

    更新日期:2020-06-30
  • Fenchel–Nielsen coordinates on the augmented moduli space of anti-de Sitter structures
    Math. Z. (IF 0.881) Pub Date : 2020-06-30
    Andrea Tamburelli

    In this paper we combine our recent work on regular globally hyperbolic maximal anti-de Sitter structures with the classical theory of globally hyperbolic maximal Cauchy-compact anti-de Sitter manifolds in order to define an augmented moduli space. Moreover, we introduce a coordinate system in this space that resembles the complex Fenchel–Nielsen coordinates for hyperbolic quasi-Fuchsian manifolds

    更新日期:2020-06-30
  • The Liouville theorem for $$p$$p -harmonic functions and quasiminimizers with finite energy
    Math. Z. (IF 0.881) Pub Date : 2020-06-24
    Anders Björn, Jana Björn, Nageswari Shanmugalingam

    We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite pth power energy in a (not necessarily complete) metric measure space equipped with a globally doubling measure supporting a global \(p\)-Poincaré inequality. The geometric conditions are that either (a) the measure has a sufficiently strong volume growth at infinity, or (b) the metric space is annularly

    更新日期:2020-06-25
  • Correction to: Kauffman type invariants for tied links
    Math. Z. (IF 0.881) Pub Date : 2020-06-19
    Francesca Aicardi, Jesús Juyumaya

    In the original publication, there are missing symbols in Theorem 1 and two missing lines in Theorem 3 (cf. https://arxiv.org/pdf/1607.04841v5.pdf).

    更新日期:2020-06-22
  • Conformal metric sequences with integral-bounded scalar curvature
    Math. Z. (IF 0.881) Pub Date : 2020-06-16
    Yuxiang Li, Zhipeng Zhou

    Let (M, g) be a smooth compact Riemiannian manifold without boundary and \(g_k\) be a metric conformal to g. Suppose \(\text{ vol }(M,g_k)+\Vert R_k\Vert _{L^p(M,g_k)}\frac{n}{2}\). We will use the 3-circles theorem to study the bubble tree convergence of \(g_k\).

    更新日期:2020-06-16
  • Twisted doubling integrals for classical groups
    Math. Z. (IF 0.881) Pub Date : 2020-06-16
    Yuanqing Cai

    We describe the twisted doubling integrals of Cai–Friedberg–Ginzburg–Kaplan in a conceptual way. This also extends the construction to the quaternionic unitary groups. We carry out the unfolding argument uniformly in this article. To do so, we define a family of degenerate Whittaker coefficients that are suitable in this setup and study some of their properties. We also prove certain related global

    更新日期:2020-06-16
  • Nonarchimedean components of non-endoscopic automorphic representations for quasisplit Sp ( N ) and O ( N )
    Math. Z. (IF 0.881) Pub Date : 2020-06-15
    Bin Xu

    Arthur classified the discrete automorphic representations of symplectic and orthogonal groups over a number field by that of the general linear groups. In this classification, those that are not from endoscopic lifting correspond to pairs \((\phi , b)\), where \(\phi \) is an irreducible unitary cuspidal automorphic representation of some general linear group and b is an integer. In this paper, we

    更新日期:2020-06-15
  • The $$RO(C_2)$$RO(C2) -graded cohomology of $$C_2$$C2 -surfaces in $$\underline{{\mathbb {Z}}/2}$$Z/2̲ -coefficients
    Math. Z. (IF 0.881) Pub Date : 2020-06-15
    Christy Hazel

    A surface with an involution can be viewed as a \(C_2\)-space where \(C_2\) is the cyclic group of order two. Up to equivariant isomorphism, all involutions on surfaces were classified in Bujalance et al. (Math Z 211:461–478, 1992) and recently classified using equivariant surgery in Dugger (J Homotopy Relat Struct 14(4):919–992, 2019). We use the classification given in Dugger (2019) to compute the

    更新日期:2020-06-15
  • Line bundles on rigid varieties and Hodge symmetry
    Math. Z. (IF 0.881) Pub Date : 2020-06-13
    David Hansen, Shizhang Li

    We prove several related results on the low-degree Hodge numbers of proper smooth rigid analytic varieties over non-archimedean fields. Our arguments rely on known structure theorems for the relevant Picard varieties, together with recent advances in p-adic Hodge theory. We also define a rigid analytic Albanese naturally associated with any smooth proper rigid space.

    更新日期:2020-06-13
  • Zero-one Schubert polynomials
    Math. Z. (IF 0.881) Pub Date : 2020-06-10
    Alex Fink, Karola Mészáros, Avery St. Dizier

    We prove that if \(\sigma \in S_m\) is a pattern of \(w \in S_n\), then we can express the Schubert polynomial \(\mathfrak {S}_w\) as a monomial times \(\mathfrak {S}_\sigma \) (in reindexed variables) plus a polynomial with nonnegative coefficients. This implies that the set of permutations whose Schubert polynomials have all their coefficients equal to either 0 or 1 is closed under pattern containment

    更新日期:2020-06-10
  • Homogeneous Levi non-degenerate hypersurfaces in $${{\mathbb {C}}}^3$$C3
    Math. Z. (IF 0.881) Pub Date : 2020-06-09
    Boris Doubrov, Alexandr Medvedev, Dennis The

    We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in \({{\mathbb {C}}}^3\) with symmetry algebra of dimension \(\ge 6\).

    更新日期:2020-06-09
  • On Lisbon integrals
    Math. Z. (IF 0.881) Pub Date : 2020-06-08
    Daniel Barlet, Teresa Monteiro Fernandes

    We introduce new complex analytic integral transforms, the Lisbon Integrals, which naturally arise in the study of the affine space \(\mathbb {C}^k\) of unitary polynomials \(P_s(z)\) where \(s\in \mathbb {C}^k\) and \(z\in \mathbb {C}\), \(s_i\) identified to the i-th symmetric function of the roots of \(P_s(z)\). We completely determine the \(\mathscr {D}\)-modules (or systems of partial differential

    更新日期:2020-06-08
  • Gamma factors for the Asai cube representation
    Math. Z. (IF 0.881) Pub Date : 2020-06-08
    Shih-Yu Chen

    We prove an equality between the gamma factors for the Asai cube representation of \(\mathrm{R}_{E/F}\mathrm{{GL}}_2\) defined by the Weil–Deligne representations and by the local zeta integrals of Ikeda and Piatetski-Shapiro–Rallis, where E is an étale cubic algebra over a local field F of characteristic zero.

    更新日期:2020-06-08
  • Existence of similar point configurations in thin subsets of $${\mathbb {R}}^d$$Rd
    Math. Z. (IF 0.881) Pub Date : 2020-06-05
    Allan Greenleaf, Alex Iosevich, Sevak Mkrtchyan

    We prove the existence of similar and multi-similar point configurations (or simplexes) in sets of fractional Hausdorff dimension in Euclidean space. Let \(d \ge 2\) and \(E\subset {{{\mathbb {R}}} }^d\) be a compact set. For \(k\ge 1\), define $$\begin{aligned} \Delta _k(E)=\left\{ \left( |x^1-x^2|, \dots , |x^i-x^j|,\dots , |x^k-x^{k+1}|\right) : \left\{ x^i\right\} _{i=1}^{k+1}\subset E\right\}

    更新日期:2020-06-05
  • On the Gan–Gross–Prasad problem for finite unitary groups
    Math. Z. (IF 0.881) Pub Date : 2020-06-05
    Dongwen Liu, Zhicheng Wang

    In this paper we study the Gan–Gross–Prasad problem for unitary groups over finite fields. Our results provide complete answers for unipotent representations, and we obtain the explicit branching of these representations.

    更新日期:2020-06-05
  • $$\mathbf {L^p\rightarrow L^q}$$Lp→Lq bounds for spherical maximal operators
    Math. Z. (IF 0.881) Pub Date : 2020-06-05
    T. Anderson, K. Hughes, J. Roos, A. Seeger

    Let \(f\in L^p({\mathbb {R}}^d)\), \(d\ge 3\), and let \(A_t f(x)\) be the average of f over the sphere with radius t centered at x. For a subset E of [1, 2] we prove close to sharp \(L^p\rightarrow L^q\) estimates for the maximal function \(\sup _{t\in E} |A_t f|\). A new feature is the dependence of the results on both the upper Minkowski dimension of E and the Assouad dimension of E. The result

    更新日期:2020-06-05
  • $$d\mathbb {Z}$$dZ -Cluster tilting subcategories of singularity categories
    Math. Z. (IF 0.881) Pub Date : 2020-06-05
    Sondre Kvamme

    For an exact category \({{\mathcal {E}}}\) with enough projectives and with a \(d\mathbb {Z}\)-cluster tilting subcategory, we show that the singularity category of \({{\mathcal {E}}}\) admits a \(d\mathbb {Z}\)-cluster tilting subcategory. To do this we introduce cluster tilting subcategories of left triangulated categories, and we show that there is a correspondence between cluster tilting subcategories

    更新日期:2020-06-05
  • On Tian–Todorov lemma and its applications to deformation of CR-structures
    Math. Z. (IF 0.881) Pub Date : 2020-06-04
    Sheng Rao, Yongpan Zou

    We give a new Tian–Todorov lemma on deformations of CR-structures and use it to reprove the deformation unobstructedness of normal compact strongly pseudoconvex CR-manifold under the assumption of \(d'd''\)-lemma, more faithfully following Tian–Todorov’s approach.

    更新日期:2020-06-04
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