Mario Santilli

collaborators

4 papers

math.DG2026

When all parallel sets of a $C^{1}$ -hypersurface are nowhere $C^{1}$ -regular

Mario Santilli

We prove a necessary and sufficient condition for a $C^{1}$ -hypersurface to have all parallel sets nowhere $C^{1}$ -regular. As a corollary, we deduce that for a generic $C^{1}$ -reg…

math.AP2026

Perpendicularity and Locality for Codimension-One Varifolds with Bounded Anisotropic Mean Curvature

SÅawomir KolasiÅski, Mario Santilli

Suppose $F$ is an integrand associated with a uniformly convex $C^{3}$ -norm, and $V$ is a $n$ -dimensional varifold in an open subset of $R^{n + 1}$ such…

math.AP2026

Bubbling of almost critical points of anisotropic isoperimetric problems with degenerating ellipticity

Mario Santilli

Given a sequence of uniformly convex norms $I ¨ _{h}$ on $R^{n + 1}$ converging to an arbitrary norm $I ¨ $ , we prove rigidity of $L^{1}$ -accumulation points of sequences of…

math.DG2025

Alexandrov sphere theorems for $W^{2, n}$ -hypersurfaces

Mario Santilli, Paolo Valentini

In this paper we extend Alexandrov's sphere theorems for higher-order mean curvature functions to $W^{2, n}$ -regular hypersurfaces under a general degenerate elliptic condition. T…

When all parallel sets of a C1-hypersurface are nowhere C1-regular

Perpendicularity and Locality for Codimension-One Varifolds with Bounded Anisotropic Mean Curvature

Bubbling of almost critical points of anisotropic isoperimetric problems with degenerating ellipticity

Alexandrov sphere theorems for W2,n-hypersurfaces

When all parallel sets of a $C^{1}$ -hypersurface are nowhere $C^{1}$ -regular

Alexandrov sphere theorems for $W^{2, n}$ -hypersurfaces