https://neckpinch.com/authors/vedansh-arya/New arXiv papers by Vedansh Arya, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2603.24091/arxiv:2603.24091Wed, 25 Mar 2026 00:00:00 GMTVedansh Arya, Seongmin Jeon, Vesa Julin — The recent work of Morini-Oronzio-Spadaro and the third author shows that, in three dimensions, a flat-flow solution of the volume-preserving mean curvature flow that converges to a single ball, which is the case for instance when the initial perimeter is less than that of two disjoint balls, converges exponentially fast in Hausdorff distance. In this paper we strengthen this result by proving that after a finite time the flow becomes smooth, satisfies the equation in the classical sense and converges exponentially fast to the limiting ball in every C^k-norm. In the proof we develop a version of Brakke's epsilon regularity theorem adapted to our setting and derive the necessary nonlinear PDE estimates directly at the level of the discrete minimizing-movement scheme. The same result holds in the planar case.Mean curvature flowVolume-preserving & constrained flowsSingularitiesWeak & singular flowsLong-time existence & convergence https://neckpinch.com/papers/2503.05399/arxiv:2503.05399Fri, 07 Mar 2025 00:00:00 GMTVedansh Arya, Daniele De Gennaro, Anna Kubin — We study the asymptotic behavior of flat flow solutions to the periodic and planar two-phase Mullins-Sekerka flow and area-preserving curvature flow. We show that flat flows converge to either a finite union of equally sized disjoint disks or to a finite union of disjoint strips or to the complement of these configurations exponentially fast. A key ingredient in our approach is the derivation of a sharp quantitative Alexandrov inequality for periodic smooth sets.Other curvature flowsVolume-preserving & constrained flowsLong-time existence & convergence