Alexandrov curvature of convex hypersurfaces in Hilbert space

TL;DR

This paper proves that convex hypersurfaces in infinite-dimensional Hilbert spaces possess nonnegative Alexandrov curvature, extending finite-dimensional results to an infinite-dimensional setting.

Contribution

It generalizes Buyalo's finite-dimensional convex hypersurface curvature result to the infinite-dimensional Hilbert space context.

Findings

Convex hypersurfaces in Hilbert spaces have nonnegative Alexandrov curvature.

Extension of finite-dimensional curvature results to infinite-dimensional spaces.

Abstract

It is shown that convex hypersurfaces in Hilbert spaces have nonnegative Alexandrov curvature. This extends an earlier result of Buyalo for convex hypersurfaces in Riemannian manifolds of finite dimension.