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arXiv · 1807.11100

Convergence of Curve Shortening Flow to Translating Soliton

Beomjun Choi·Kyeongsu Choi·Panagiota Daskalopoulos
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Abstract

This paper concerns with the asymptotic behavior of complete non-compact convex curves embedded in $\mathbb{R}^2$ under the $\alpha$-curve shortening flow for exponents $\alpha >\frac12$. We show that any such curve having in addition its two ends asymptotic to two parallel lines, converges under $\alpha$-curve shortening flow to the unique translating soliton whose ends are asymptotic to the same parallel lines. This is a new result even in the standard case $\alpha=1$, and we prove for all exponents up to the critical case $\alpha>\frac12$.

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Beomjun Choi, Kyeongsu Choi, Panagiota Daskalopoulos. 2018-07-29. Convergence of Curve Shortening Flow to Translating Soliton. https://arxiv.org/abs/1807.11100

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