Mathematical Sciences: Mean Curvature Problems in Euclidean Space and Topics in Geometric Analysis

Korevaar教授将继续将先前开发的解析和拓扑技术应用于常平均曲率曲面的几何结构。将进一步应用于具有共适性的常数标量曲率度量的研究。解决这些问题有望在经典表面理论中带来许多有趣的突破，而以前应用的方法并不总是成功的。另一个问题是继续利用拉普拉斯算子的谱理论发展的流形分解方法来研究“形状”现象。PI还致力于在这一研究领域培养几名研究生。

Professor Korevaar will continue to apply previously developed analytic and topological techniques to the geometric structure of constant mean curvature surfaces. Further applications will be made to the study of constant scalar curvature metrics with conformality. resolving these problems is expected to lead to a number of interesting breakthroughs in classical surface theory where previously applied methods were not always successful. Another problem is to continue the manifold decomposition methods developed via spectral theory of the Laplace operator to investigate `shape' phenomena. The PI is also committed to training several graduate students in this area of research.