Curve shortening flows on rotational surfaces generated by monotone convex functions

2022/02/21 by Naotoshi Fujihara, Fujihara, Naotoshi
Mathematics · #53E10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2202.09956

openalex publication_date 2022/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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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