Work

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

Year: 2025

Type: article

Abstract: We prove that the proximal unit normal bundle of the subgraph of a $W^{2,n} $ -function carries a natural structure of Legendrian cycle. This result is used to obtain an Alexandrov-type sphere theorem for hypersurfaces in $ \mathbf{R}^{n+1} $ , which are locally graphs of arbitrary $W^{2,n} $ -functions. We also extend the classical umbilicality theorem to $ W^{2,1} $ -graphs, under the Lusin (N) condition for the graph map.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2025.10047

Authors: Mario Santilli, Paolo Valentini

Institution: University of L'Aquila

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni