Curve shortening flows in warped product manifolds

Hengyu Zhou

Curve shortening flows in warped product manifolds

Differential Geometry 2017-01-24 v2

Authors: Hengyu Zhou

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.

Keywords

curve shortening flow warped product manifold riemannian manifold geodesic convergence S^1 graph long-time existence

Cite

@article{arxiv.1511.07553,
  title  = {Curve shortening flows in warped product manifolds},
  author = {Hengyu Zhou},
  journal= {arXiv preprint arXiv:1511.07553},
  year   = {2017}
}

Comments

Final Version. (The proof of Proposition 5.1 is revised). Accepted by Proceedings of AMS

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