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Conformal solitons for the mean curvature flow in hyperbolic space Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2024-03-15 L. Mari, J. Rocha de Oliveira, A. Savas-Halilaj, R. Sodré de Sena
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Multiple tubular excisions and large Steklov eigenvalues Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2024-03-10 Jade Brisson
Given a closed Riemannian manifold M and \(b\ge 2\) closed connected submanifolds \(N_j\subset M\) of codimension at least 2, we prove that the first nonzero eigenvalue of the domain \(\Omega _\varepsilon \subset M\) obtained by removing the tubular neighbourhood of size \(\varepsilon \) around each \(N_j\) tends to infinity as \(\varepsilon \) tends to 0. More precisely, we prove a lower bound in
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Rigidity results of weighted area-minimizing hypersurfaces Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2024-03-05 Sanghun Lee, Sangwoo Park, Juncheol Pyo
In this paper, we prove two rigidity results of hypersurfaces in n-dimensional weighted Riemannian manifolds with weighted scalar curvature bounded from below. Firstly, we establish a splitting theorem for the n-dimensional weighted Riemannian manifold via a weighted area-minimizing hypersurface. Secondly, we observe the topological invariance of the weighted stable hypersurface when the ambient weighted
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Correction to: Hypercohomologies of truncated twisted holomorphic de Rham complexes Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2024-02-29
Abstract In the original article [1], Theorem 1.2 (Künneth theorem) is incorrect.
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Some regularity of submetries Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2024-02-21 Alexander Lytchak
We discuss regularity statements for equidistant decompositions of Riemannian manifolds and for the corresponding quotient spaces. We show that any stratum of the quotient space has curvature locally bounded from both sides.
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Subgraphs of BV functions on RCD spaces Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2024-02-17
Abstract In this work, we extend classical results for subgraphs of functions of bounded variation in \(\mathbb R^n\times \mathbb R\) to the setting of \({\textsf{X}}\times \mathbb R\) , where \({\textsf{X}}\) is an \({\textrm{RCD}}(K,N)\) metric measure space. In particular, we give the precise expression of the push-forward onto \({\textsf{X}}\) of the perimeter measure of the subgraph in \({\textsf{X}}\times
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Some remarks on almost Hermitian functionals Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2024-01-31 Tedi Draghici, Cem Sayar
We study critical points of natural functionals on various spaces of almost Hermitian structures on a compact manifold \(M^{2n}\). We present a general framework, introducing the notion of gradient of an almost Hermitian functional. As a consequence of the diffeomorphism invariance, we show that a Schur’s type theorem still holds for general almost Hermitian functionals, generalizing a known fact for
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On subelliptic harmonic maps with potential Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2024-01-30 Yuxin Dong, Han Luo, Weike Yu
Let \((M,H,g_H;g)\) be a sub-Riemannian manifold and (N, h) be a Riemannian manifold. For a smooth map \(u: M \rightarrow N\), we consider the energy functional \(E_G(u) = \frac{1}{2} \int _M[|\textrm{d}u_\text {H}|^2 - 2\,G(u)] \textrm{d}V_M\), where \(\textrm{d}u_\text {H}\) is the horizontal differential of u, \(G:N\rightarrow \mathbb {R}\) is a smooth function on N. The critical maps of \(E_G(u)\)
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Almost CR manifolds with contracting CR automorphism Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2024-01-23
Abstract In this paper, we deal with a strongly pseudoconvex almost CR manifold with a CR contraction. We will prove that the stable manifold of the CR contraction is CR equivalent to the Heisenberg group model.
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Instability of a family of examples of harmonic maps Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2024-01-09 Nobumitsu Nakauchi
The radial map u(x) \(=\) \(\frac{x}{\Vert x\Vert }\) is a well-known example of a harmonic map from \({\mathbb {R}}^m\,-\,\{0\}\) into the spheres \({\mathbb {S}}^{m-1}\) with a point singularity at x \(=\) 0. In Nakauchi (Examples Counterexamples 3:100107, 2023), the author constructed recursively a family of harmonic maps \(u^{(n)}\) into \({\mathbb {S}}^{m^n-1}\) with a point singularity at the
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Modular geodesics and wedge domains in non-compactly causal symmetric spaces Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-12-31 Vincenzo Morinelli, Karl-Hermann Neeb, Gestur Ólafsson
We continue our investigation of the interplay between causal structures on symmetric spaces and geometric aspects of Algebraic Quantum Field Theory. We adopt the perspective that the geometric implementation of the modular group is given by the flow generated by an Euler element of the Lie algebra (an element defining a 3-grading). Since any Euler element of a semisimple Lie algebra specifies a canonical
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From complex contact structures to real almost contact 3-structures Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-12-12 Eder M. Correa
We prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application, we provide several new examples of manifolds which admit taut contact circles, taut and round almost cosymplectic 2-spheres, and almost hypercontact (metric) structures. These examples generalize the well-known examples of contact circles defined by the Liouville-Cartan
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Optimal transport approach to Michael–Simon–Sobolev inequalities in manifolds with intermediate Ricci curvature lower bounds Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-12-13 Kai-Hsiang Wang
We generalize McCann’s theorem of optimal transport to a submanifold setting and use it to prove Michael–Simon–Sobolev inequalities for submanifolds in manifolds with lower bounds on intermediate Ricci curvatures. The results include a variant of the sharp Michael–Simon–Sobolev inequality in Brendle’s (arXiv:2009.13717) when the intermediate Ricci curvatures are nonnegative.
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Immersions of Sasaki–Ricci solitons into homogeneous Sasakian manifolds Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-12-14 R. Mossa, G. Placini
We discuss local Sasakian immersion of Sasaki–Ricci solitons (SRS) into fiber products of homogeneous Sasakian manifolds. In particular, we prove that SRS locally induced by a large class of fiber products of homogeneous Sasakian manifolds are, in fact, \(\eta \)-Einstein. The results are stronger for immersions into Sasakian space forms. Moreover, we show an example of a Kähler–Ricci soliton on \(\mathbb
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Families of degenerating Poincaré–Einstein metrics on $$\mathbb {R}^4$$ Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-12-06 Carlos A. Alvarado, Tristan Ozuch, Daniel A. Santiago
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Commutativity of quantization with conic reduction for torus actions on compact CR manifolds Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-11-29 Andrea Galasso
We define conic reductions \(X^{\textrm{red}}_{\nu }\) for torus actions on the boundary X of a strictly pseudo-convex domain and for a given weight \(\nu \) labeling a unitary irreducible representation. There is a natural residual circle action on \(X^{\textrm{red}}_{\nu }\). We have two natural decompositions of the corresponding Hardy spaces H(X) and \(H(X^{\textrm{red}}_{\nu })\). The first one
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Berglund–Hübsch transpose rule and Sasakian geometry Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-11-16 Ralph R. Gomez
We apply the Berglund–Hübsch transpose rule from BHK mirror symmetry to show that to an \(n-1\)-dimensional Calabi–Yau orbifold in weighted projective space defined by an invertible polynomial, we can associate four (possibly) distinct Sasaki manifolds of dimension \(2n+1\) which are \(n-1\)-connected and admit a metric of positive Ricci curvature. We apply this theorem to show that for a given K3
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Sasaki–Einstein 7-manifolds and Orlik’s conjecture Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-11-16 Jaime Cuadros Valle, Joe Lope Vicente
We study the homology groups of certain 2-connected 7-manifolds admitting quasi-regular Sasaki–Einstein metrics, among them, we found 52 new examples of Sasaki–Einstein rational homology 7-spheres, extending the list given by Boyer et al. (Ann Inst Fourier 52(5):1569–1584, 2002). As a consequence, we exhibit new families of positive Sasakian homotopy 9-spheres given as cyclic branched covers, determine
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Boundary properties for a Monge-Ampère equation of prescribed affine Gauss curvature Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-11-16 Yadong Wu
Considering a Monge-Ampère equation with prescribed affine Gauss curvature, we first show the completeness of centroaffine metric on the convex domain and derive a gradient estimate of the convex solution and then give different orders of two eigenvalues of the Hessian with respect to the distance function. We also show that the curvature of level sets of the convex solution is uniformly bounded, and
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The metric structure of compact rank-one ECS manifolds Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-10-26 Andrzej Derdzinski, Ivo Terek
Pseudo-Riemannian manifolds with nonzero parallel Weyl tensor which are not locally symmetric are known as ECS manifolds. Every ECS manifold carries a distinguished null parallel distribution \(\mathcal {D}\), the rank \(d\in \{1,2\}\) of which is referred to as the rank of the manifold itself. Under a natural genericity assumption on the Weyl tensor, we fully describe the universal coverings of compact
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Harmonic flow of geometric structures Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-10-17 Eric Loubeau, Henrique N. Sá Earp
We give a twistorial interpretation of geometric structures on a Riemannian manifold, as sections of homogeneous fibre bundles, following an original insight by Wood (Differ Geom Appl 19:193–210, 2003). The natural Dirichlet energy induces an abstract harmonicity condition, which gives rise to a geometric gradient flow. We establish a number of analytic properties for this flow, such as uniqueness
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On the index of a free-boundary minimal surface in Riemannian Schwarzschild-AdS Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-10-04 Justin Corvino, Elene Karangozishvili, Deniz Ozbay
We consider the index of a certain non-compact free-boundary minimal surface with boundary on the rotationally symmetric minimal sphere in the Schwarzschild-AdS geometry with \(m>0\). As in the Schwarzschild case, we show that in dimensions \(n\ge 4\), the surface is stable, whereas in dimension three, the stability depends on the value of the mass \(m>0\) and the cosmological constant \(\Lambda <0\)
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Solution to the n-bubble problem on $$\mathbb {R}^1$$ with log-concave density Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-09-28 John Ross
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Compactness of harmonic maps of surfaces with regular nodes Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-09-25 Woongbae Park
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Dirichlet problem for harmonic maps from strongly rectifiable spaces into regular balls in $${\text {CAT}}(1)$$ spaces Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-09-16 Yohei Sakurai
In this note, we study the Dirichlet problem for harmonic maps from strongly rectifiable spaces into regular balls in \({\text {CAT}}(1)\) space. Under the setting, we prove that the Korevaar–Schoen energy admits a unique minimizer.
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Modified conformal extensions Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-09-13 Matthias Hammerl, Katja Sagerschnig, Josef Šilhan, Vojtěch Žádník
We present a geometric construction and characterization of 2n-dimensional split-signature conformal structures endowed with a twistor spinor with integrable kernel. The construction is regarded as a modification of the conformal Patterson–Walker metric construction for n-dimensional projective manifolds. The characterization is presented in terms of the twistor spinor and an integrability condition
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On the intrinsic and extrinsic boundary for metric measure spaces with lower curvature bounds Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-08-31 Vitali Kapovitch, Xingyu Zhu
We show that if an Alexandrov space X has an Alexandrov subspace \({\bar{\Omega }}\) of the same dimension disjoint from the boundary of X, then the topological boundary of \({\bar{\Omega }}\) coincides with its Alexandrov boundary. Similarly, if a noncollapsed \({{\,\textrm{RCD}\,}}(K,N)\) space X has a noncollapsed \({{\,\textrm{RCD}\,}}(K,N)\) subspace \({\bar{\Omega }}\) disjoint from boundary
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Hadamard expansions for powers of causal Green’s operators and “resolvents” Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-08-29 Lennart Ronge
The Hadamard expansion describes the singularity structure of Green’s operators associated with a normally hyperbolic operator P in terms of Riesz distributions (fundamental solutions on Minkowski space, transported to the manifold via the exponential map) and Hadamard coefficients (smooth sections in two variables, corresponding to the heat Kernel coefficients in the Riemannian case). In this paper
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Explicit harmonic morphisms and p-harmonic functions from the complex and quaternionic Grassmannians Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-08-24 Elsa Ghandour, Sigmundur Gudmundsson
We construct explicit complex-valued p-harmonic functions and harmonic morphisms on the classical compact symmetric complex and quaternionic Grassmannians. The ingredients for our construction method are joint eigenfunctions of the classical Laplace–Beltrami and the so-called conformality operator. A known duality principle implies that these p-harmonic functions and harmonic morphisms also induce
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Quantitative version of Weyl’s law Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-08-20 Nikhil Savale
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Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-08-08 DongSeon Hwang, Shin-young Kim, Kyeong-Dong Park
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Almost contact metric manifolds with certain condition Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-08-08 Benaoumeur Bayour, Gherici Beldjilali, Moulay Larbi Sinacer
The object of this article is to study a new class of almost contact metric structures which are integrable but non normal. Secondly, we explain a method of construction for normal manifold starting from a non-normal but integrable manifold. Illustrative examples are given.
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Prescribed mean curvature flow of non-compact space-like Cauchy hypersurfaces Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-08-02 Giuseppe Gentile, Boris Vertman
In this paper we consider the prescribed mean curvature flow of a non-compact space-like Cauchy hypersurface of bounded geometry in a generalized Robertson–Walker space-time. We prove that the flow preserves the space-likeness condition and exists for infinite time. We also prove convergence in the setting of manifolds with boundary. Our discussion generalizes previous work by Ecker, Huisken, Gerhardt
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The metric completion of the space of vector-valued one-forms Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-08-01 Nicola Cavallucci, Zhe Su
The space of full-ranked one-forms on a smooth, orientable, compact manifold (possibly with boundary) is metrically incomplete with respect to the induced geodesic distance of the generalized Ebin metric. We show a distance equality between the induced geodesic distances of the generalized Ebin metric on the space of full-ranked one-forms and the corresponding Riemannian metric defined on each fiber
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Products of manifolds with fibered corners Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-07-27 Chris Kottke, Frédéric Rochon
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Anticanonically balanced metrics and the Hilbert–Mumford criterion for the $$\delta _m$$ -invariant of Fujita–Odaka Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-07-12 Yoshinori Hashimoto
We prove that the stability condition for Fano manifolds defined by Saito–Takahashi, given in terms of the sum of the Ding invariant and the Chow weight, is equivalent to the existence of anticanonically balanced metrics. Combined with the result by Rubinstein–Tian–Zhang, we obtain the following algebro-geometric corollary: the \(\delta _m\)-invariant of Fujita–Odaka satisfies \(\delta _m >1\) if and
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Calabi type functionals for coupled Kähler–Einstein metrics Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-07-10 Satoshi Nakamura
We introduce the coupled Ricci–Calabi functional and the coupled H-functional which measure how far a Kähler metric is from a coupled Kähler–Einstein metric in the sense of Hultgren–Witt Nyström. We first give corresponding moment weight type inequalities which estimate each functional in terms of algebraic invariants. Secondly, we give corresponding Hessian formulas for these functionals at each critical
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Compact surfaces with boundary with prescribed mean curvature depending on the Gauss map Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-07-03 Antonio Bueno, Rafael López
Given a \(C^1\) function \(\mathcal {H}\) defined in the unit sphere \(\mathbb {S}^2\), an \(\mathcal {H}\)-surface M is a surface in the Euclidean space \(\mathbb {R}^3\) whose mean curvature \(H_M\) satisfies \(H_M(p)=\mathcal {H}(N_p)\), \(p\in M\), where N is the Gauss map of M. Given a closed simple curve \(\Gamma \subset \mathbb {R}^3\) and a function \(\mathcal {H}\), in this paper we investigate
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Anti-quasi-Sasakian manifolds Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-06-26 D. Di Pinto, G. Dileo
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Levi-flat CR structures on compact Lie groups Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-06-21 Howard Jacobowitz, Max Reinhold Jahnke
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Integral decompositions of varifolds Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-06-21 Hsin-Chuang Chou
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Extra-twisted connected sum $$G_2$$ -manifolds Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-06-12 Johannes Nordström
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Existence results for a super Toda system Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-06-07 Aleks Jevnikar, Ruijun Wu
We solve a super Toda system on a closed Riemann surface of genus \(\gamma >1\) and with some particular spin structures. This generalizes the min–max methods and results for super Liouville equations and gives new existence results for super Toda systems.
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Homogeneous Einstein metrics and butterflies Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-06-02 Christoph Böhm, Megan M. Kerr
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Sobolev inequalities and convergence for Riemannian metrics and distance functions Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-06-01 B. Allen, E. Bryden
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On non-compact gradient solitons Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-05-24 Antonio W. Cunha, Erin Griffin
In this paper, we extend existing results for generalized solitons, called q-solitons, to the complete case by considering non-compact solitons. By placing regularity conditions on the vector field X and curvature conditions on M, we are able to use the chosen properties of the tensor q to see that such non-compact q-solitons are stationary and q-flat. We conclude by applying our results to the examples
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Pseudo-Kähler and pseudo-Sasaki structures on Einstein solvmanifolds Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-04-24 Diego Conti, Federico Alberto Rossi, Romeo Segnan Dalmasso
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Laplace eigenvalues of ellipsoids obtained as analytic perturbations of the unit sphere Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-04-25 Anandateertha G. Mangasuli, Aditya Tiwari
The Euclidean unit sphere in dimension n minimizes the first positive eigenvalue of the Laplacian among all the compact, Riemannian manifolds of dimension n with Ricci curvature bounded below by \(n-1\) as a consequence of Lichnerowicz’s theorem. The eigenspectrum of the Laplacian is given by a non-decreasing sequence of real numbers tending to infinity. In dimension two, we prove that such an inequality
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Remarks on astheno-Kähler manifolds, Bott-Chern and Aeppli cohomology groups Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-04-24 Ionuţ Chiose, Rareş Răsdeaconu
We provide a new cohomological obstruction to the existence of astheno-Kähler metrics on compact complex manifolds. Several results of independent interests regarding the Bott-Chern and Aeppli cohomology groups are presented and relevant examples are discussed.
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Normalized Yamabe flow on manifolds with bounded geometry Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-04-19 Bruno Caldeira, Luiz Hartmann, Boris Vertman
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Kummer-type constructions of almost Ricci-flat 5-manifolds Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-04-13 Chanyoung Sung
A smooth closed manifold M is called almost Ricci-flat if $$\begin{aligned} \inf _g||\text {Ric}_g||_\infty \cdot \text {diam}_g(M)^2=0 \end{aligned}$$ where \(\text {Ric}_g\) and \(\text {diam}_g\), respectively, denote the Ricci tensor and the diameter of g and g runs over all Riemannian metrics on M. By using Kummer-type method, we construct a smooth closed almost Ricci-flat nonspin 5-manifold M
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The Lax equation and weak regularity of asymptotic estimate Lie groups Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-04-05 Maximilian Hanusch
We investigate the Lax equation in the context of infinite-dimensional Lie algebras. Explicit solutions are discussed in the sequentially complete asymptotic estimate context, and an integral expansion (sums of iterated Riemann integrals over nested commutators with correction term) is derived for the situation that the Lie algebra is inherited by an infinite-dimensional Lie group in Milnor’s sense
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Geodesics on a K3 surface near the orbifold limit Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-04-03 Jørgen Olsen Lye
This article studies Kummer K3 surfaces close to the orbifold limit. We improve upon estimates for the Calabi–Yau metrics due to Kobayashi. As an application, we study stable closed geodesics. We use the metric estimates to show how there are generally restrictions on the existence of such geodesics. We also show how there can exist stable, closed geodesics in some highly symmetric circumstances due
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Conformal Bach flow Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-03-30 Jiaqi Chen, Peng Lu, Jie Qing
In this article we introduce conformal Bach flow and establish its well-posedness on closed manifolds. We also obtain its backward uniqueness. To give an attempt to study the long-time behavior of conformal Bach flow, assuming that the curvature and the pressure function are bounded, global and local Shi’s type \(L^2\)-estimate of derivatives of curvatures is derived. Furthermore, using the \(L^2\)-estimate
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Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-03-21 Stefano Borghini, Lorenzo Mazzieri
In Hwang and Yun (Ann Glob Anal Geom 62(3):507–532, 2022), an estimate for skew-symmetric 2-tensors was claimed. Soon after, this estimate has been exploited to claim powerful classification results: Most notably, it has been employed to propose a proof of a Black Hole Uniqueness Theorem for vacuum static spacetimes with positive scalar curvature (Xu and Ye in Invent Math 33(2):64, 2022) and in connection
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Dispersive equations on asymptotically conical manifolds: time decay in the low-frequency regime Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-03-06 Viviana Grasselli
On an asymptotically conical manifold, we prove time decay estimates for the flow of the Schrödinger wave and Klein–Gordon equations via some differentiability properties of the spectral measure. To keep the paper at a reasonable length, we limit ourselves to the low-energy part of the spectrum, which is the one that dictates the decay rates. With this paper, we extend sharp estimates that are known
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Classification of left-invariant Einstein metrics on $$\textrm{SL}(2,\mathbb {R})\times \textrm{SL}(2,\mathbb {R})$$ that are bi-invariant under a one-parameter subgroup Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-03-02 Vicente Cortés, Jeremias Ehlert, Alexander S. Haupt, David Lindemann
We classify all left-invariant pseudo-Riemannian Einstein metrics on \(\textrm{SL}(2,\mathbb {R})\times \textrm{SL}(2,\mathbb {R})\) that are bi-invariant under a one-parameter subgroup. We find that there are precisely two such metrics up to homothety, the Killing form and a nearly pseudo-Kähler metric.
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Correction to: Hypercohomologies of truncated twisted holomorphic de Rham complexes Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-02-27 Lingxu Meng
Abstract In the original article (Meng in Ann Glob Anal Geom 57(4):519–535, 2020. https://doi.org/10.1007/s10455-020-09711-y), Theorem 1.2 (Künneth theorem) is incorrect. We pointed which step is wrong in the proof of Meng (2020, Theorem 1.2) by an example and explain why (Meng 2020, Theorem 1.2) is not true for general cases.
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Rigidity results for Riemannian twistor spaces under vanishing curvature conditions Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-02-23 G. Catino, D. Dameno, P. Mastrolia
In this paper, we provide new rigidity results for four-dimensional Riemannian manifolds and their twistor spaces. In particular, using the moving frame method, we prove that \(\mathbb {C}\mathbb {P}^3\) is the only twistor space whose Bochner tensor is parallel; moreover, we classify Hermitian Ricci-parallel and locally symmetric twistor spaces and we show the nonexistence of conformally flat twistor
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Gauss maps of harmonic and minimal great circle fibrations Ann. Glob. Anal. Geom. (IF 0.7) Pub Date : 2023-02-13 Ioannis Fourtzis, Michael Markellos, Andreas Savas-Halilaj
We investigate Gauss maps associated to great circle fibrations of the euclidean unit 3-sphere \(\mathbb {S}^3\). We show that the associated Gauss map to such a fibration is harmonic, respectively minimal, if and only if the unit vector field generating the great circle foliation is harmonic, respectively minimal. These results can be viewed as analogues of the classical theorem of Ruh and Vilms about