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.File | Dimensione | Formato | |
---|---|---|---|
2304.11129v1.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
369.36 kB
Formato
Adobe PDF
|
369.36 kB | Adobe PDF | Visualizza/Apri |
s00526-023-02610-7.pdf
non disponibili
Tipologia:
Versione finale editoriale
Licenza:
NON PUBBLICO - accesso privato/ristretto
Dimensione
503.31 kB
Formato
Adobe PDF
|
503.31 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.