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  • Conformal Patterson–Walker metrics
    Asian J. Math. (IF 0.542) Pub Date : 
    Matthias Hammerl; Katja Sagerschnig; Josef Šilhan; Arman Taghavi-Chabert; Vojtěch Žádník

    The classical Patterson–Walker construction of a split-signature (pseudo-)Riemannian structure from a given torsion-free affine connection is generalized to a construction of a split-signature conformal structure from a given projective class of connections. A characterization of the induced structures is obtained. We achieve a complete description of Einstein metrics in the conformal class formed

    更新日期:2020-07-20
  • On dissolving knot surgery $4$-manifolds under a $\mathbb{CP}^2$-connected sum
    Asian J. Math. (IF 0.542) Pub Date : 
    Hakho Choi; Jongil Park; Ki-Heon Yun

    In this article we prove that, if $X$ is a smooth $4$-manifold containing an embedded double node neighborhood, all knot surgery $4$-manifolds $X_K$ are mutually diffeomorphic to each other after a connected sum with $\mathbb{CP}^2$. Hence, by applying to the simply connected elliptic surface $E(n)$, we also show that every knot surgery $4$-manifold $E(n)_K$ is almost completely decomposable.

    更新日期:2020-07-20
  • Real spinor bundles and real Lipschitz structures
    Asian J. Math. (IF 0.542) Pub Date : 
    C. I. Lazaroiu; C. S. Shahbazi

    Let $(M, g)$ be a pseudo-Riemannian manifold of arbitrary dimension and signature. We prove that there exist mutually quasi-inverse equivalences between the groupoid of weakly faithful real pinor bundles on $(M, g)$ and the groupoid of weakly faithful real Lipschitz structures on $(M, g)$, from which follows that every bundle of weakly faithful real Clifford modules is associated to a real Lipschitz

    更新日期:2020-07-20
  • The $Q_{ \alpha}$-restriction problem
    Asian J. Math. (IF 0.542) Pub Date : 
    Z. Wang; J. Xiao; Y. Zhou

    Let $\alpha \in [0, 1)$ and $\Omega$ be an open connected subset of $\mathbb{R}^{n \geq 2}$. This paper shows that the $Q_{\alpha}$-restriction problem $Q_{\alpha} \vert {}_{\Omega} = \mathscr{Q}_{\alpha} (\Omega)$ is solvable if and only if $\Omega$ is an Ahlfors $n$-regular domain; i.e., $\operatorname{vol} \bigl ( B(x, r) \cap \Omega \bigr ) \gtrsim r^n$ for any Euclidean ball $B(x, r)$ with center

    更新日期:2020-07-20
  • $F$-manifolds, multi-flat structures and Painlevé transcendents
    Asian J. Math. (IF 0.542) Pub Date : 
    Alessandro Arsie; Paolo Lorenzoni

    In this paper we study $F$-manifolds equipped with multiple flat connections and multiple $F$-products, that are required to be compatible in a suitable sense. Multi-flat $F$-manifolds are the analogue for $F$-manifolds of Frobenius manifolds with multi-Hamiltonian structures. In the semisimple case, we show that a necessary condition for the existence of such multiple flat connections can be expressed

    更新日期:2020-07-20
  • Semistable Higgs bundles on Calabi–Yau manifolds
    Asian J. Math. (IF 0.542) Pub Date : 2019-12-01
    U. Bruzzo; V. Lanza; A. Lo Giudice

    We provide a partial classification of semistable Higgs bundles over simply connected Calabi–Yau manifolds. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved for K3 and Enriques surfaces, and some related classes of surfaces.

    更新日期:2019-12-01
  • Proof of a Gromov conjecture on the infinitesimal invertibility of the metric-inducing operators
    Asian J. Math. (IF 0.542) Pub Date : 2019-12-01
    Roberto de Leo

    We prove a conjecture of Gromov about non-free isometric immersions.

    更新日期:2019-12-01
  • An Alexandrov theorem in Minkowski spacetime
    Asian J. Math. (IF 0.542) Pub Date : 2019-12-01
    Oussama Hijazi; Sebastián Montiel; Simon Raulot

    In this paper, using a spinorial approach, we generalize a theorem à la Alexandrov of Wang, Wang and Zhang [WWZ] to closed codimension-two spacelike submanifolds in the Minkowski spacetime for an adapted CMC condition.

    更新日期:2019-12-01
  • Bi-Lipschitz geometry of contact orbits in the boundary of the nice dimensions
    Asian J. Math. (IF 0.542) Pub Date : 2019-12-01
    Saurabh Trivedi; Maria Aparecida Soares Ruas

    Mather proved that the smooth stability of smooth maps between manifolds is a generic condition if and only if the pair of dimensions of the manifolds are ‘nice dimensions’ while topological stability is a generic condition in any pair of dimensions. And, by a result of du Plessis and Wall $C^1$-stability is also a generic condition precisely in the nice dimensions. We address the question of bi‑Lipschitz

    更新日期:2019-12-01
  • Quenched weighted moments of a supercritical branching process in a random environment
    Asian J. Math. (IF 0.542) Pub Date : 2019-12-01
    Yuejiao Wang; Yingqiu Li; Quansheng Liu; Zaiming Liu

    We consider a supercritical branching process $(Z_n)$ in an independent and identically distributed random environment $\xi = (\xi_n)$. Let $W$ be the limit of the natural martingale $W_n = Z_n / E_\xi Z_n , n \geq 0$, where $E_\xi$ denotes the conditional expectation given the environment $\xi$. We find a necessary and sufficient condition for the existence of quenched weighted moments of $W$ of the

    更新日期:2019-12-01
  • Deformations from a given Kähler metric to a twisted cscK metric
    Asian J. Math. (IF 0.542) Pub Date : 2019-12-01
    Yu Zeng

    In [3], X. Chen proposed a continuity path aiming to attack the existence problem of the constant scalar curvature Kähler(cscK) metric. He also proved the openness of the path at $t \in (0, 1)$ by the standard implicit function theorem on solutions of fourth order PDE. However, the openness at $t = 0$ is quite different in nature and it is in fact a deformation result from the solution of a second

    更新日期:2019-12-01
  • Stability inequalities for Lawson cones
    Asian J. Math. (IF 0.542) Pub Date : 2019-12-01
    Zhenhua Liu

    In [1], Guido De Philippis and Francesco Maggi proved global quadratic stability inequalities and derived explicit lower bounds for the first eigenvalues of the stability operators for all area-minimizing Lawson cones $M_{kh}$, except for those with\[(k, h), (h, k) \in S = \lbrace (3, 5), (2, 7), (2, 8), (2, 9), (2, 10), (2, 11) \rbrace \; \textrm{.}\]We proved the corresponding inequalities and lower

    更新日期:2019-12-01
  • Outermost apparent horizons diffeomorphic to unit normal bundles
    Asian J. Math. (IF 0.542) Pub Date : 2019-12-01
    Mattias Dahl; Eric Larsson

    Given a submanifold $S \subset \mathbb{R}^n$ of codimension at least three, we construct an asymptotically Euclidean Riemannian metric on $\mathbb{R}^n$ with nonnegative scalar curvature for which the outermost apparent horizon is diffeomorphic to the unit normal bundle of $S$.

    更新日期:2019-12-01
  • Stability of anti-canonically balanced metrics
    Asian J. Math. (IF 0.542) Pub Date : 2019-12-01
    Shunsuke Saito; Ryosuke Takahashi

    We study the asymptotic behavior of quantized Ding functionals along Bergman geodesic rays and prove that the slope at infinity can be expressed in terms of Donaldson–Futaki invariants and Chow weights. Based on the slope formula, we introduce a new algebro-geometric stability on Fano manifolds and show that the existence of anti-canonically balanced metrics implies our stability. The relation between

    更新日期:2019-12-01
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