https://neckpinch.com/authors/dohyun-kwon/New arXiv papers by Dohyun Kwon, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2405.08296/arxiv:2405.08296Tue, 14 May 2024 00:00:00 GMTEric Kim, Dohyun Kwon — We study the motion of sets by anisotropic curvature under a volume constraint in the plane. We establish the exponential convergence of the area-preserving anisotropic flat flow to a disjoint union of Wulff shapes of equal area, the critical point of the anisotropic perimeter functional. This is an anisotropic analogue of the results in the isotropic case studied in. The novelty of our approach is in using the Cahn-Hoffman map to parametrize boundary components as small perturbations of the Wulff shape. In addition, we show that certain reflection comparison symmetries are preserved by the flat flow, which lets us obtain uniform bounds on the distance between the convergent profile and the initial data.Mean curvature flowVolume-preserving & constrained flowsAnisotropic & nonlocal flowsLong-time existence & convergence https://neckpinch.com/papers/2108.01244/arxiv:2108.01244Tue, 03 Aug 2021 00:00:00 GMTJiwoong Jang, Dohyun Kwon, Hiroyoshi Mitake, Hung Vinh Tran — Here, we study a level-set forced mean curvature flow with the homogeneous Neumann boundary condition. We first show that the solution is Lipschitz in time and locally Lipschitz in space. Then, under an additional condition on the forcing term, we prove that the solution is globally Lipschitz. We obtain the large time behavior of the solution in this setting and study the large time profile in some specific situations. Finally, we give two examples demonstrating that the additional condition on the forcing term is sharp, and without it, the solution might not be globally Lipschitz.Mean curvature flowVolume-preserving & constrained flowsHomogeneous spacesBoundaries & non-compactFree boundary & capillary