Curve shortening flows in warped product manifolds

Zhou, Hengyu

doi:10.1090/proc/13661

Curve shortening flows in warped product manifolds
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by Hengyu Zhou

Proc. Amer. Math. Soc. 145 (2017), 4503-4516

DOI: https://doi.org/10.1090/proc/13661

Published electronically: April 12, 2017

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Abstract:

We study curve shortening flows in two types of warped product manifolds. These manifolds are $\mathbb {S}^1 \times N$ with two types of warped metrics where $\mathbb {S}^1$ is the unit circle in $\mathbb {R}^2$ and $N$ is a closed Riemannian manifold. If the initial curve is a graph over $\mathbb {S}^1$, then its curve shortening flow exists for all times and finally converges to a geodesic closed curve.

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