An expository paper on rearrangement and co-area inequalities that leaves the manifold version as definitions and contains multiple invalid proof steps.
Isoperimetric Inequalities: Differential Geometric and An alytic Perspectives , Cambridge University Press, 2001
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Symmetric Rearrangement and Geometric Inequalities on Riemannian Manifolds
An expository paper on rearrangement and co-area inequalities that leaves the manifold version as definitions and contains multiple invalid proof steps.