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arXiv · 1805.12540

Evolution of Contractions between Non-Compact Manifolds

Felix Lubbe
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Abstract

Let $N$ be a complete manifold with bounded geometry, such that $\sec_N\le -\sigma < 0$ for some positive constant $\sigma$. We investigate the mean curvature flow of the graphs of smooth length-decreasing maps $f:\mathbb{R}^m\to N$. In this case, the solution exists for all times and the evolving submanifold stays the graph of a length-decreasing map $f_t$. We further prove uniform decay estimates for all derivatives of order $\ge 2$ of $f_t$ along the flow.

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Felix Lubbe. 2018-05-29. Evolution of Contractions between Non-Compact Manifolds. https://arxiv.org/abs/1805.12540

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