$(\mathbf{M},cr^\gamma,\delta)$-minimizing curve regularity

Abstract

This is a new proof that $(\mathbf{M},Cr^\gamma,\delta)$-minimizing sets $S$ are pieces of $\mathcal{C}^{1,\gamma/2}$ curves, $0<\gamma\leqslant1$. To obtain this result, the almost monotonicity property is established for balls centered on $S$ or not. Furthermore it is proved that almost minimizing sets fulfill the epiperimetric inequality.