Geometric and Analytic Problems on Real Hypersurfaces

复变量函数在数学、物理和工程的许多领域中都扮演着重要的角色。这个项目将在复杂变量理论中发展一些相互关联的主题，这些主题可能有助于在该理论中开辟新的方向，并建立从该理论到其他数学领域的桥梁。预计该项目将通过学生和年轻研究者的参与，帮助建立人类基础设施。主要研究者要解决的具体问题包括与费弗曼测度和韦伯斯特曲率有关的几何和变分问题；多复变量超定边值问题的偏微分方程作为边界相容条件的研究考虑射影对偶的复欧几里得域边界上竞争部分复结构的研究Hardy空间上庞加莱型不等式的常数研究并研究了全纯常系数偏微分方程解的边界范数。

Functions of complex variables play an essential role throughout much of mathematics and in many parts of physics and engineering. This project will develop a number of interrelated topics in complex variables theory which may serve to open up new directions within that theory and to build bridges from that theory to other mathematical areas. It is expected that the project will help to build human infrastructure by involving students and younger investigators.The specific problems to be addressed by the principal investigator include geometric and variational problems connected to Fefferman measure and Webster curvature; the study of partial differential equations serving as boundary compatibility conditions for various overdetermined boundary value problems arising in several complex variables; the study of competing partial complex structures on boundaries of certain complex euclidean domains arising from considerations of projective duality; the study of constants for of Poincare-type inequalities on Hardy spaces; and the study of boundary norms for solutions of holomorphic constant-coefficient partial differential equations.