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Convexity of hypersurfaces with vanishing curvature

Published on:

29 August 2023

Primary Category:

Differential Geometry

Paper Authors:

Mohammad Ghomi


Key Details

Proves convexity of a class of hypersurfaces in nonpositively curved manifolds

Uses Gauss-Codazzi equations and Alexandrov geometry techniques

Extends theorems of Chern-Lashof and Greene-Wu-Gromov

Settles a problem posed by M. Gromov on surfaces of least total curvature

Demonstrates rigidity of hypersurfaces via intrinsic and extrinsic geometry

AI generated summary

Convexity of hypersurfaces with vanishing curvature

This paper proves that closed, infinitesimally convex hypersurfaces in certain nonpositively curved manifolds bound convex regions, generalizing classic results about convexity. It has implications for rigidity and finiteness properties of these ambient manifolds.

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