Geometric curvature bounds in Riemannian manifolds with boundary

Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.

doi:10.1090/S0002-9947-1993-1113693-1

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.

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