Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds

2019/08/26 by Ghomi, Mohammad, Spruck, Joel · 1 citation
#49Q15 (Secondary) #52A38 #53C20 #58J05 (Primary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1908.09814

Abstract

We obtain an explicit formula for comparing total curvature of level sets of functions on Riemannian manifolds, and develop some applications of this result to the isoperimetric problem in spaces of nonpositive curvature.

Cited by

• Continuity of total curvatures of Riemannian hypersurfaces

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