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

Jiuzhou Huang; Jiawei Liu

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arXiv · 2106.14779

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

Jiuzhou Huang·Jiawei Liu

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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.

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Jiuzhou Huang, Jiawei Liu. 2021-06-28. Ricci flow starting from an embedded closed convex surface in $\mathbb{R}^3$. https://arxiv.org/abs/2106.14779

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