Published Paper

Inserted: 24 apr 2023
Last Updated: 7 oct 2024

Journal: Calculus of Variations and Partial Differential Equations
Year: 2023
Doi: https://link.springer.com/article/10.1007/s00526-023-02610-7

Abstract:

We introduce a symmetric (log-)epiperimetric inequality, generalizing the standard epiperimetric inequality, and we show that it implies a growth-decay for the associated energy: as the radius increases energy decays while negative and grows while positive. One can view the symmetric epiperimetric inequality as giving a log-convexity of energy, analogous to the 3-annulus lemma or frequency formula. We establish the symmetric epiperimetric inequality for some free-boundary problems and almost-minimizing currents, and give some applications including a ``propagation of graphicality'' estimate, uniqueness of blow-downs at infinity, and a local Liouville-type theorem.