LOCAL REGULARITY PROPERTIES OF ALMOST- AND QUASIMINIMAL SETS WITH A SLIDING BOUNDARY CONDITION

Guy David (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We study the boundary regularity of almost minimal and quasiminimal sets that satisfy sliding boundary conditions. The competitors of a set $E$ are defined as $F = \varphi_1(E)$, where $\{ \varphi_t \}$ is a one parameter family of continuous mappings defined on $E$, and that preserve a given collection of boundary pieces. We generalize known interior regularity results, and in particular we show that the quasiminimal sets are locally Ahlfors-regular, rectifiable, and some times uniformly rectifiable, that our classes are stable under limits, and that for almost minimal sets the density of Hausdorff measure in balls centered on the boundary is almost nondecreasing.

Mots clés: Minimal sets; Almost minimal sets; Almgren restricted or quasiminimal sets; Sliding boundary condition; Hausdorff measure

Domaines: Analyse classique [math.CA]

Guy David. LOCAL REGULARITY PROPERTIES OF ALMOST- AND QUASIMINIMAL SETS WITH A SLIDING BOUNDARY CONDITION. 2014. ⟨hal-00924010⟩