# Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above

Research paper by Stephanie B. Alexander, Richard L. Bishop

Indexed on: 22 Nov '05Published on: 22 Nov '05Published in: Mathematics - Differential Geometry

#### Abstract

A Gauss equation is proved for subspaces of Alexandrov spaces of curvature bounded above by K. That is, a subspace of extrinsic curvature less than or equal to A, defined by a cubic inequality on the difference of arc and chord, has intrinsic curvature less than or equal to K+A^2. Sharp bounds on injectivity radii of subspaces, new even in the Riemannian case, are derived.