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

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

2005-11-22

arxiv.org/abs/math/0511570v1

Mathematics

Differential Geometry

17 pages, 4 figures

Scientific paper

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.

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