Preprint

Inserted: 23 feb 2022
Last Updated: 23 feb 2022

Pages: 61
Year: 2022

Abstract:

We consider the isoperimetric problem defined on the whole $\mathbb{R}^n$ by the Allen--Cahn energy functional. For non-degenerate double well potentials, we prove sharp quantitative stability inequalities of quadratic type which are uniform in the length scale of the phase transitions. We also derive a rigidity theorem for critical points analogous to the classical Alexandrov's theorem for constant mean curvature boundaries.

Download:

• ACRn41.pdf