Manifolds with Density

Frank Morgan, Williams College

Thursday September 1, 4:00PM, Herman Brown 227


Riemannian manifolds with density often arise in an ad hoc way throughout mathematics. For example, in calculus, volumes and surfaces of revolution about the z-axis in R3 are represented by areas and curves in the halfplane {(x,z): x >= 0} with density 2 pi x. An important example for probabilists is "Gauss space", Euclidean space with Gaussian density. Some Riemannian geometry, such as Ricci curvature and the Levy-Gromov isoperimetric theorem, generalizes to manifolds with density. The classical model space, the sphere, is supplanted by Gauss space, the new model.

Reference: Frank Morgan, Manifolds with density, Notices Amer. Math. Soc. 52 (Sept, 2005), 848-853.