Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above
Stephanie B. Alexander, Richard L. Bishop
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+A2. Sharp bounds on injectivity radii of subspaces, new even in the Riemannian case, are derived.
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