Geometric Analysis, Applications in the Analysis of Some Applied Math PDE's, and Developing Geometry Courses for Freshmen and Math Education Majors

9704488汉该项目位于黎曼几何学的一般领域。研究人员将继续研究与标量曲率和高斯曲率、几何偏微分方程组(涡旋单方程)以及调和映射到负曲面的几何有关的问题。该项目还包含一个涉及本科生几何课程的教育部分。几何偏微分方程使用几何分析中不同领域的技术，如调和映射和黎曼几何来求解在各种背景下出现的微分方程。例如，涡旋片方程与空气和其他流体中涡旋的演化以及超导中的相变有关。

9704488 Han The project lies in the general area of Riemannian geometry. The investigator is to pursue questions related to scalar and Gauss curvatures, geometric PDEs (vortex sheet equation), and the geometry of harmonic maps into negatively curved surfaces. The project also contains an education component involving the undergraduate geometry curriculum. Geometric partial differential equations use techniques from various areas in geometric analysis such as harmonic maps and Riemannian geometry to solve differential equations arising in a variety of contexts. For example, the vortex sheet equation is related to the evolution of vortices in the air and other fluids as well as to phase transitions in super-conductivity.