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math.DG2026
Sharp dynamical isoperimetric principle for mean curvature flow
Beomjun Choi, Wenkui Du, Seung Chul Park +1
In this paper, we establish a sharp dynamical isoperimetric principle for weak mean curvature flow. We prove that, among weak mean curvature flows with fixed area of initial smooth…
math.AP2026
Second order estimates on transition layers for the Allen-Cahn equation with homogeneous Neumann boundary conditions: Part I - Boundary-orthogonal transition layers
Akashdeep Dey, Wenkui Du, Davide Parise +1
We study stable solutions of the Allen-Cahn equation with homogeneous Neumann boundary condition on Riemannian manifolds with boundary in the regime where the transition layers mee…