## 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.