Answers are grounded in this paper and cite their sources.
New findings demonstrate Alexandrov-type sphere theorem for W^{2,n} hypersurfaces, suggesting further study on umbilicality conditions.
We prove that the proximal unit normal bundle of the subgraph of a W2,n -function carries a natural structure of Legendrian cycle . This result is used to obtain an Alexandrov-type sphere theorem for hypersurfaces in Rⁿ⁺¹ , which are locally graphs of arbitrary W2,n -functions. We also extend the classical umbilicality theorem to W2,1 -graphs, under the Lusin (N) condition for the graph map.
No takes yet. Share an insight, caveat, or question.
Santilli et al. (2025) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: