Abstract

It is shown that convex hypersurfaces in Hilbert space forms have corresponding lower bounds on Alexandrov curvature. This extends earlier work of Buyalo, Alexander, Kapovitch, and Petrunin for convex hypersurfaces in Riemannian manifolds of finite dimension.

Author information

Contact details are reproduced from the original publication and may be historical.

Jonathan Dahl

Dept. of Mathematics, Lafayette College, 229 Pardee Hall, Easton, PA 18042, U.S.A.

dahlj@lafayette.edu

Keywords

  • Convex hypersurfaces
  • Alexandrov curvature
  • Hilbert spaces

Mathematics Subject Classification

53C45, 53C23

Suggested citation

J. Dahl. “Alexandrov Curvature of Convex Hypersurfaces in Hilbert Space Forms.” Journal of Convex Analysis 25 (2018), No. 3, 781–788.

Copyright Banach Press 2018