In this paper, the curve shortening flow in a general Riemannian manifold is studied, Altschuler's results about the flow for space curves are generalized. For any n-dimensional (n >= 2) Riemannian manifold (M, g) with some natural assumptions, we prove the planar phenomenon when the curve shortening flow blows up.
Singularities of the Curve Shortening Flow in a Riemannian Manifold
Pan, Shujing
First
2021-01-01
Abstract
In this paper, the curve shortening flow in a general Riemannian manifold is studied, Altschuler's results about the flow for space curves are generalized. For any n-dimensional (n >= 2) Riemannian manifold (M, g) with some natural assumptions, we prove the planar phenomenon when the curve shortening flow blows up.
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