理学院数理讲坛（2016年第十四讲）
报告题目：Euler sprays and Wasserstein geometry of the space of shapes
报告专家：刘建国（Jian-Guo Liu）教授 （美国 Duke University）
报告时间：2016年5月17日下午 15:00—16:00
报告地点：阳明学院 303
摘要：
We study a distance between shapes defined by minimizing the integral of kinetic energy along transport pathsconstrained to measures with characteristic-function densities. The formal geodesic equations for this shape distanceare Euler equations for incompressible, inviscid potential flowof fluid with zero pressure and surface tension on the free boundary.
The minimization problem exhibits an instability associated with microdroplet formation, with the following outcomes: Shape distance is equal to Wasserstein distance. Furthermore, any two shapes of equal volume can be approximately connected by an Euler spray---a countable superposition of ellipsoidal droplet solutions of incompressible Euler equations. Every Wasserstein geodesic between shape densities is a weak limit of Euler sprays.Each Wasserstein geodesic is also the unique minimizer of a relaxed least-action principle for a fluid-vacuum mixture. This is a joint work with Bob Pego and Dejan Slepcev of CMU.
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