均值凸锥的均值凸平滑化

IF 2.4 1区数学 Q1 MATHEMATICS Geometric and Functional Analysis Pub Date : 2024-02-01 DOI:10.1007/s00039-024-00666-x

Zhihan Wang

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引用次数: 0

摘要

我们证明，任何最小化超锥都可以扰动为欧几里得空间中一个适当嵌入的光滑最小化超曲面的一面，并且每个粘性均值凸锥都可以在无穷大附近找到一个与之渐近的适当嵌入的光滑均值凸自展开器。这两点共同证实了劳森的猜想（Geom.）

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Mean Convex Smoothing of Mean Convex Cones

We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space, and every viscosity mean convex cone admits a properly embedded smooth mean convex self-expander asymptotic to it near infinity. These two together confirm a conjecture of Lawson (Geom. Meas. Theor. Calcu. Var. 44:441, 1986, Problem 5.7).

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来源期刊

Geometric and Functional Analysis 数学-数学

CiteScore

3.70

自引率

4.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.

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