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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Geometric curvature bounds in Riemannian manifolds with boundary


Authors: Stephanie B. Alexander, I. David Berg and Richard L. Bishop
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1113693-1
Article copyright: © Copyright 1993 American Mathematical Society