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arXiv · 1511.07553

Curve shortening flows in warped product manifolds

Hengyu Zhou
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Abstract

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

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Hengyu Zhou. 2015-11-24. Curve shortening flows in warped product manifolds. https://arxiv.org/abs/1511.07553

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