We prove a new logarithmic epiperimetric inequality for multiplicity-one stationary cones with isolated singularity by flowing any given trace in the radial direction along appropriately chosen directions. In contrast to previous epiperimetric inequalities for minimal surfaces (eg work of Reifenberg, Taylor and White), we need no a priori assumptions on the structure of the cone (eg integrability). If the cone is integrable (not only through rotations), we recover the classical epiperimetric inequality. As a consequence we deduce a new regularity result for almost area-minimizing currents at singular points where at least one blowup is a multiplicity-one cone with isolated singularity. This result is similar to the one for stationary varifolds of Leon Simon (1983), but independent from it since almost-minimizers do not satisfy any equation.
(Log-)epiperimetric inequality and regularity over smooth cones for almost area-minimizing currents
Velichkov, B
2019-01-01
Abstract
We prove a new logarithmic epiperimetric inequality for multiplicity-one stationary cones with isolated singularity by flowing any given trace in the radial direction along appropriately chosen directions. In contrast to previous epiperimetric inequalities for minimal surfaces (eg work of Reifenberg, Taylor and White), we need no a priori assumptions on the structure of the cone (eg integrability). If the cone is integrable (not only through rotations), we recover the classical epiperimetric inequality. As a consequence we deduce a new regularity result for almost area-minimizing currents at singular points where at least one blowup is a multiplicity-one cone with isolated singularity. This result is similar to the one for stationary varifolds of Leon Simon (1983), but independent from it since almost-minimizers do not satisfy any equation.File | Dimensione | Formato | |
---|---|---|---|
preprint G&T.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
234.63 kB
Formato
Adobe PDF
|
234.63 kB | Adobe PDF | Visualizza/Apri |
Version of record G&T.pdf
solo utenti autorizzati
Tipologia:
Versione finale editoriale
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
404.22 kB
Formato
Adobe PDF
|
404.22 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.