https://neckpinch.com/authors/inwon-kim/New arXiv papers by Inwon Kim, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2012.13839/arxiv:2012.13839Sun, 27 Dec 2020 00:00:00 GMTInwon Kim, Dohyun Kwon, Norbert Požár — In this work we consider the global existence of volume-preserving crystalline curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address global existence and regularity of the flow for smooth anisotropies. For the non-smooth case we establish global existence results for the types of anisotropies known to be globally well-posed.Mean curvature flowOther curvature flowsVolume-preserving & constrained flowsAnisotropic & nonlocal flowsWeak & singular flowsLong-time existence & convergence https://neckpinch.com/papers/1809.09343/arxiv:1809.09343Tue, 25 Sep 2018 00:00:00 GMTHongwei Gao, Inwon Kim — In this paper, we investigate the large time behavior of interfaces moving with motion law V = −κ+ g(x), where g is positive, Lipschitz and ℤⁿ-periodic. It turns out that the behavior of the interface can be characterized by its head and tail speed, which depends continuously on its overall direction of propagation ν. If head speed equals tail speed at a given direction ν, the interface has a unique large-scale speed in that direction. In general the interface develops linearly growing "long fingers" in the direction where the equality breaks down. We discuss these results in both general setting and in laminar setting, where further results are obtained due to regularity properties of the flow.Mean curvature flow https://neckpinch.com/papers/1808.04922/arxiv:1808.04922Tue, 14 Aug 2018 00:00:00 GMTInwon Kim, Dohyun Kwon — We study the evolution of star-shaped sets in volume preserving mean curvature flow. Constructed by approximate minimizing movements, our solutions preserve a strong version of star-shapedness. We also show that the solutions converges to a ball as time goes to infinity. For asymptotic behavior of the solutions we use the gradient flow structure of the problem, whereas a modified notion of viscosity solutions is introduced to study the geometric properties of the flow by moving planes method.Mean curvature flowVolume-preserving & constrained flowsWeak & singular flows