CURVE SHORTENING FLOWS ON ROTATIONAL SURFACES GENERATED BY MONOTONE CONVEX FUNCTIONS

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2023-01-01 DOI:10.2206/kyushujm.77.179

Naotoshi FUJIHARA

引用次数: 1

Abstract

In this paper, we study curve shortening flows on rotational surfaces in ℝ3. We assume that the surfaces have negative Gauss curvatures and that some condition related to the Gauss curvature and the curvature of an embedded curve holds on them. Under these assumptions, we prove that the curve remains a graph over the parallels of the rotational surface along the flow. Also, we prove the comparison principle and the long-time existence of the flow.

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由单调凸函数生成的旋转表面上的曲线缩短流

本文研究了在旋转曲面上的曲线缩短流。我们假设曲面具有负高斯曲率，并且与高斯曲率和嵌入曲线的曲率有关的某些条件适用于它们。在这些假设下，我们证明了曲线仍然是沿流动的旋转表面的平行线上的图形。并证明了比较原理和流的长期存在性。

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

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.