Geometric curvature bounds in Riemannian manifolds with boundary
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- by Stephanie B. Alexander, I. David Berg and Richard L. Bishop PDF
- Trans. Amer. Math. Soc. 339 (1993), 703-716 Request permission
Abstract:
An Alexandrov upper bound on curvature for a Riemannian manifold with boundary is proved to be the same as an upper bound on sectional curvature of interior sections and of sections of the boundary which bend away from the interior. As corollaries those same sectional curvatures are related to estimates for convexity and conjugate radii; the Hadamard-Cartan theorem and Yau’s isoperimetric inequality for spaces with negative curvature are generalized.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 339 (1993), 703-716
- MSC: Primary 53C21; Secondary 53C20
- DOI: https://doi.org/10.1090/S0002-9947-1993-1113693-1
- MathSciNet review: 1113693