https://neckpinch.com/authors/dongyeong-ko/New arXiv papers by Dongyeong Ko, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2309.09896/arxiv:2309.09896Mon, 18 Sep 2023 00:00:00 GMTDongyeong Ko — We prove that a free boundary curve shortening flow on closed surfaces with a strictly convex boundary remains noncollapsed for a finite time in the sense of the reflected chord-arc profile introduced by Langford-Zhu. This shows that such flow converges to free boundary embedded geodesic in infinite time, or shrinks to a round half-point on the boundary. As a consequence, we prove the existence of two free boundary embedded geodesics on a Riemannian 2-disk with a strictly convex boundary. Moreover, we prove that there exists a simple closed geodesic with Morse Index 1 and 2. This settles the free boundary analog of Grayson's theorem.Curve shorteningSingularities(Non)collapsingSurfacesFree boundary & capillary