Mathematical Sciences: Geometric Variational Problems and Related PDE Questions

两位研究者将分析几何偏微分方程研究中出现的问题。我们将研究几何极值的渐近性问题，包括最小曲面方程和更一般的拟线性椭圆方程的全解的生长性质问题。他还将致力于解决长期存在的威尔莫猜想。第二名研究者将研究极小曲面奇异集的结构，调和映射在奇异点附近的渐近行为，以及极小子流形的拓扑类型。两位研究者将分析包括理解偏微分方程如何作用于最小曲面的问题。这些方程包括多个变量函数的导数，并且经常有其应用数学的起源。最小表面是普通肥皂膜的数学家模型。近年来，将偏微分方程应用于最小曲面的研究活动呈爆炸式增长。

Two investigators will analyze problems arising from the study of geometric partial differential equations. One will study questions related to asymptotics for geometric extrema, including questions about growth properties of entire solutions of the minimal surface equation and more general quasilinear elliptic equations. He will also work toward a solution of the long-standing Willmore conjecture. The second investigator will study the structure of singular sets of minimal surfaces, asymptotic behavior of harmonic maps near singularities, and topological types of minimal submanifolds. Both investigators will analyze problems which involve understanding how partial differential equations act on minimal surfaces. These equations include derivatives of functions of more than one variable and frequently have their origins in applied mathematics. Minimal surfaces are the mathematician's model of common soap films. In recent years the use of partial differential equations in connection with minimal surfaces has seen an explosion of research activity.