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Journal of Convex Analysis 25 (2018), No. 3, 781--788
Copyright Heldermann Verlag 2018

Alexandrov Curvature of Convex Hypersurfaces in Hilbert Space Forms

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

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.

Keywords: Convex hypersurfaces, Alexandrov curvature, Hilbert spaces.

MSC: 53C45, 53C23

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