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Curve shortening flows in warped product manifolds


Author: Hengyu Zhou
Journal: Proc. Amer. Math. Soc. 145 (2017), 4503-4516
MSC (2010): Primary 53C44
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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Additional Information

Hengyu Zhou
Affiliation: Department of Mathematics, Sun Yat-sen University, No. 135, Xingang Xi Road, Guangzhou, 510275, People’s Republic of China
Email: hyuzhou84@yahoo.com

DOI: https://doi.org/10.1090/proc/13661
Received by editor(s): November 17, 2015
Received by editor(s) in revised form: November 6, 2016
Published electronically: April 12, 2017
Communicated by: Michael Wolf
Article copyright: © Copyright 2017 American Mathematical Society

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