Geometric and Analytic Problems on Real Hypersurfaces

复变函数在数学的大部分内容以及物理和工程的许多部分中起着重要的作用。 这个项目将开发一些相互关联的主题在复变量理论，这可能有助于开辟新的方向，在该理论和建立桥梁，从该理论到其他数学领域。 预期该项目将通过让学生和较年轻的研究人员参与，帮助建立人力基础设施，主要研究人员将处理的具体问题包括：与费曼测度和韦伯斯特曲率有关的几何和变分问题;研究偏微分方程作为若干复变量中各种超定边值问题的边界相容性条件;研究某些复杂的欧几里德域边界上的部分复杂结构，这些复杂结构是由投影对偶引起的; 2研究哈代空间上的庞加莱型不等式的常数; 3研究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.