Euler sprays and Wasserstein geometry of the space of shapes

PDE Seminar
Tuesday, April 19, 2016 - 15:05
1 hour (actually 50 minutes)
Skiles 006
Carnegie Mellon University
We will discuss a distance between shapes defined by minimizing the integral of kinetic energy along transport paths constrained to measures with characteristic-function densities. The formal geodesic equations for this shape distance are Euler equations for incompressible, inviscid flow of fluid with zero pressure and surface tension on the free boundary. We will discuss the instability that the minimization problem develops and the resulting connections to optimal transportation. The talk is based on joint work with Jian-Guo Liu (Duke) and Bob Pego (CMU).