与各向异性曲率函数有关的 Wulff 形状的稳定性

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-10-22 DOI:10.1016/j.jfa.2024.110715

Julian Scheuer , Xuwen Zhang

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引用次数: 0

摘要

对于使封闭超曲面 M 的单边邻域叶面化的函数 f，我们给出了 M 与 Wulff 形的距离的估计值，该估计值是以 f 的无迹 F-Hessian 的 Lp-norm 表示的，其中 F 是 Wulff 形的支持函数。该定理可用于证明各向异性海因茨-卡尔切不等式、各向异性亚历山德罗夫问题以及塞林型各向异性超定边界值问题的定量稳定性结果。

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Stability of the Wulff shape with respect to anisotropic curvature functionals

For a function f which foliates a one-sided neighborhood of a closed hypersurface M, we give an estimate of the distance of M to a Wulff shape in terms of the

L^{p}

-norm of the traceless F-Hessian of f, where F is the support function of the Wulff shape. This theorem is applied to prove quantitative stability results for the anisotropic Heintze-Karcher inequality, the anisotropic Alexandrov problem, as well as for the anisotropic overdetermined boundary value problem of Serrin-type.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis