Mario Santilli

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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.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

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