封闭凸平面曲线的各向异性面积保留非局部流动

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2024-01-24 DOI:10.1515/advgeom-2023-0025

Tianyu Zhao, Yunlong Yang, Yueyue Mao, Jianbo Fang

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引用次数: 0

摘要

我们考虑了封闭凸平面曲线的各向异性面积保留非局部流，它是潘、杨（《微分方程学报》，266 (2019)，3764-3786）在τ = 1时引入的模型的广义化。在此流动条件下，演化曲线保持其凸性，并收敛于 C ∞ 意义上的光滑对称严格凸平面曲线的同调。对这种流的渐近行为的分析意味着在闵科夫斯基几何框架内将一条曲线变形为另一条曲线的可能性。

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Anisotropic area-preserving nonlocal flow for closed convex plane curves

We consider an anisotropic area-preserving nonlocal flow for closed convex plane curves, which is a generalization of the model introduced by Pan and Yang (J. Differential Equations 266 (2019), 3764–3786) when τ = 1. Under this flow, the evolving curve maintains its convexity and converges to a homothety of a smooth symmetric strictly convex plane curve in the C ∞ sense. The analysis of the asymptotic behavior of this flow implies the possibility of deforming one curve into another within the framework of Minkowski geometry.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.