Ricci flow starting from an embedded closed convex surface in $\mathbb{R}^3$

Jiuzhou Huang; Jiawei Liu

Ricci flow starting from an embedded closed convex surface in $\mathbb{R}^3$

Differential Geometry 2021-06-29 v1 Analysis of PDEs Metric Geometry

Authors: Jiuzhou Huang , Jiawei Liu

Abstract

In this paper, we establish the existence and uniqueness of Ricci flow that admits an embedded closed convex surface in $\mathbb{R}^3$ as metric initial condition. The main point is a family of smooth Ricci flows starting from smooth convex surfaces whose metrics converge uniformly to the metric of the initial surface in intrinsic sense.

Keywords

ricci flow geodesic flow surfaces and embeddings

Cite

@article{arxiv.2106.14779,
  title  = {Ricci flow starting from an embedded closed convex surface in $\mathbb{R}^3$},
  author = {Jiuzhou Huang and Jiawei Liu},
  journal= {arXiv preprint arXiv:2106.14779},
  year   = {2021}
}

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