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Main Authors: Hu, Guangming, Lei, Ziping, Sun, Yu, Zhou, Puchun
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2404.05982
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author Hu, Guangming
Lei, Ziping
Sun, Yu
Zhou, Puchun
author_facet Hu, Guangming
Lei, Ziping
Sun, Yu
Zhou, Puchun
contents In this paper, we study the existence and rigidity of (degenerated) circle pattern metric with prescribed total geodesic curvatures in spherical background geometry. To find the (degenerated) circle pattern metric with prescribed total geodesic curvatures, we define some prescribed combinatorial Ricci flows and study the convergence of flows for (degenerated) circle pattern metrics. We solve the prescribed total geodesic curvature problem and provide two methods to find the degenerated circle pattern metric with prescribed total geodesic curvatures. As far as we know, this is the first degenerated result for total geodesic curvatures in spherical background geometry.
format Preprint
id arxiv_https___arxiv_org_abs_2404_05982
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The Convergence of Prescribed Combinatorial Ricci Flows for Total Geodesic Curvatures in Spherical Background Geometry
Hu, Guangming
Lei, Ziping
Sun, Yu
Zhou, Puchun
Geometric Topology
In this paper, we study the existence and rigidity of (degenerated) circle pattern metric with prescribed total geodesic curvatures in spherical background geometry. To find the (degenerated) circle pattern metric with prescribed total geodesic curvatures, we define some prescribed combinatorial Ricci flows and study the convergence of flows for (degenerated) circle pattern metrics. We solve the prescribed total geodesic curvature problem and provide two methods to find the degenerated circle pattern metric with prescribed total geodesic curvatures. As far as we know, this is the first degenerated result for total geodesic curvatures in spherical background geometry.
title The Convergence of Prescribed Combinatorial Ricci Flows for Total Geodesic Curvatures in Spherical Background Geometry
topic Geometric Topology
url https://arxiv.org/abs/2404.05982