Revista Matemática Iberoamericana
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Published online: 2017-02-22
Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditionsManuel Ritoré (1) Universidad de Granada, Spain
Let $M$ be a complete Riemannian manifold possessing a strictly convex Lipschitz continuous exhaustion function. We show that the isoperimetric profile of $M$ is a continuous and non-decreasing function. Particular cases are Hadamard manifolds and complete non-compact manifolds with strictly positive sectional curvatures.
Keywords: Strictly convex functions, isoperimetric profile, convex sets, Hadamard manifolds, positive curvature
Ritoré Manuel: Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions. Rev. Mat. Iberoam. 33 (2017), 239-250. doi: 10.4171/RMI/935