Let be a complete Riemannian manifold possessing a strictly convex Lipschitz continuous exhaustion function. We show that the isoperimetric profile of is a continuous and non-decreasing function. Particular cases are Hadamard manifolds and complete non-compact manifolds with strictly positive sectional curvatures.
Cite this article
Manuel Ritoré, Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions. Rev. Mat. Iberoam. 33 (2017), no. 1, pp. 239–250DOI 10.4171/RMI/935