Develops modified Hessian estimates under nonnegative weighted sectional curvature to obtain comparison theorems, monotonic weighted volume densities, and rigidity results for manifolds with density.
Petersen, Riemannian Geometry, 3rd ed.
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Comparison Geometry on Manifolds with Density via Modified Hessians
Develops modified Hessian estimates under nonnegative weighted sectional curvature to obtain comparison theorems, monotonic weighted volume densities, and rigidity results for manifolds with density.