Anisotropic Gauss curvature flow of complete non-compact graphs

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-09-16 DOI:10.1016/j.geomphys.2025.105648

Shujing Pan, Yong Wei

引用次数: 0

Abstract

In this paper, we consider the anisotropic α-Gauss curvature flow for complete noncompact convex hypersurfaces in the Euclidean space with the anisotropy determined by a smooth closed uniformly convex Wulff shape. We show that for all positive power

α > 0

, if the initial hypersurface is complete noncompact and locally uniformly convex, then there exists a complete, noncompact, smooth and strictly convex solution of the flow which is defined for all positive time.

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完全非紧图的各向异性高斯曲率流

本文考虑欧几里德空间中完全非紧凸超曲面的各向异性α-高斯曲率流，其各向异性由光滑闭合一致凸Wulff形状决定。我们证明了对于所有正幂α>；0，如果初始超曲面是完全非紧且局部一致凸的，则存在一个对所有正时间都有定义的流的完全、非紧、光滑和严格凸解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity