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

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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.
17 pages, 4 figures

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Differential Geometry, Metric Geometry, 53C70,53C20,53B25

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http://salesiana.dossiersoluciones.com/handle/123456789/105048

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511570
 http://arxiv.org/abs/math/0511570

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arXiv