Nonlinear Heat Equations in Geometry, Mechanics and Imaging

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

The PI intends to study the asymptotics of singular solutions to heat equations which occur in Riemannian geometry, such as Ricci flow and mean curvature flow, and also free boundary problems involving fourth order equations. Further problems of interest to the PI are related to the formulation of the Monge-Kantorovich mass-transfer problem, and in particular variations thereof which may appear in medical imaging problems. Differential Geometry and partial differential equations (PDE) play a central role in modern science and engineering. The PI is interested both in studying these subjects from the "pure-mathematics" point of view, and in collaborating with engineers and scientists to find new applications of geometry and PDE to practical problems. Particular applied areas of interest to the PI involve the automated processing of images (brain scans, virtual colonoscopy, etc) generated in the medical sciences.