Higher order isoperimetric inequalities - an approach via the method of optimal transport
Presenter
August 22, 2013
Keywords:
- isoperimetric inequality
- optimal transport
- higher order
- k-convexity
- Monge mass transport
- Monge-Ampere equation
- non-linear PDE
- Ricci curvature
- second fundamental form
- Gaussian curvature
- symmetric functions
MSC:
- 32W20
- 82C70
- 34B10
- 37-xx
- 37Fxx
- 37Gxx
- 52B60
- 53C21
Abstract
One of the method to derive sharp isoperimetric inequality for domains in the Euclidean is to apply the method of optimal transport; in this talk, I will report some recent joint work with Yi Wang to extend the method to prove some higher order isoperimetric inequalities with integrands involving symmetric functions of the second fundamental form.