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.

The symmetric (log-)epiperimetric inequality and a decay-growth estimate

Velichkov, Bozhidar
2024-01-01

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.
2024
Edelen, Nick; Spolaor, Luca; Velichkov, Bozhidar
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1254556
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