Mathematical Sciences: Regularity and Singularity in Geometric Variational and Flow Problems

提出了两个相关的研究课题：能量最小化图的奇异性和曲率流。Simon开创了研究能量最小化映射的顶维奇异集的分析技术，并因此获得了Bocher奖。除了继续这项研究——这可能会导致一个重要猜想的解决，即能量的最小值是分层流形——曲率流的几个问题被提出。所提出的曲率流动问题模拟了广泛的现象，如肥皂膜动力学、不混相流体和晶体生长，并且属于非线性抛物型偏微分方程领域。

Simon 9504456 Two related topics of research are proposed: singularities of energy minimizing maps and curvature flows. Simon pioneered analytic techniques for studying the top-dimensional singular set of an energy minimizing map, for which he recently won the Bocher prize. In addition to continuing this research - which could lead to a resolution of the important conjecture asserting that minimizers of energy are stratified manifolds - several problems on curvature flows are proposed. Proposed curvature flow problems model a wide range of phenomena, such as the dynamics of soap films, immiscible fluids and crystal growth, and lie in the area of nonlinear parabolic partial differential equations.