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TITLE CONVERGENCE OF CURVE SHORTENING FLOW TO TRANSLATING SOLITON
KIAS AUTHORS Choi, Kyeongsu
JOURNAL AMERICAN JOURNAL OF MATHEMATICS, 2021
ARCHIVE  
ABSTRACT This paper concerns with the asymptotic behavior of complete non-compact convex curves embedded in R-2 under the alpha-curve shortening flow for exponents alpha > 1/2. 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 > 1/2.
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