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

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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