2018/07/29 by Beomjun Choi, Kyeongsu Choi, Choi, Beomjun +3 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1807.11100
This paper concerns with the asymptotic behavior of complete non-compact convex curves embedded in ℝ2 under the α-curve shortening flow for exponents α>\frac12. We show that any such curve having in addition its two ends asymptotic to two parallel lines, converges under α-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 α=1, and we prove for all exponents up to the critical case α>\frac12.