Document Type
Presentation
Location
Math Conference Room: College of Arts and Sciences
Start Date
10-29-2026 10:00 AM
End Date
10-29-2026 11:00 AM
Description
This talk introduces some basic concepts in several complex variables and explains the role of pseudo convexity through two fundamental topics: Hartog’s' extension phenomenon and the Levi problem. A stronger property than pseudo convexity is the existence of a plurisubharmonic defining function. Such defining functions play an important role in the study of analytic objects associated with a domain, including the regularity of the d-bar Neumann operator and the Bergman projection. The main question of this talk is whether a pseudo convex domain admits a plurisubharmonic defining function. We approach this question in two steps. First, we establish a necessary condition, and in certain cases a sufficient condition, for the existence of a defining function that is plurisubharmonic on the boundary. Second, we investigate the necessary conditions for extending this boundary plurisubharmonic into the interior of the domain.
Several Complex Variables, Pseudoconvexity, and Plurisubharmonic defining functions
Math Conference Room: College of Arts and Sciences
This talk introduces some basic concepts in several complex variables and explains the role of pseudo convexity through two fundamental topics: Hartog’s' extension phenomenon and the Levi problem. A stronger property than pseudo convexity is the existence of a plurisubharmonic defining function. Such defining functions play an important role in the study of analytic objects associated with a domain, including the regularity of the d-bar Neumann operator and the Bergman projection. The main question of this talk is whether a pseudo convex domain admits a plurisubharmonic defining function. We approach this question in two steps. First, we establish a necessary condition, and in certain cases a sufficient condition, for the existence of a defining function that is plurisubharmonic on the boundary. Second, we investigate the necessary conditions for extending this boundary plurisubharmonic into the interior of the domain.