曲线缩短流下模量的单调性

arXiv - MATH - Differential Geometry Pub Date : 2024-09-04 DOI:arxiv-2409.03098

Arjun Sobnack, Peter M. Topping

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引用次数: 0

摘要

给定平面中两条互不相交的嵌套封闭曲线，它们都在曲线缩短流的作用下演化，我们证明封闭环面的模量随时间单调递增。类似的结果在满足曲率下限的任何环境曲面中都成立。

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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Monotonicity of the modulus under curve shortening flow

Given two disjoint nested embedded closed curves in the plane, both evolving under curve shortening flow, we show that the modulus of the enclosed annulus is monotonically increasing in time. An analogous result holds within any ambient surface satisfying a lower curvature bound.

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arXiv - MATH - Differential Geometry

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