学术报告（刘炳远 5.29）

Abstract

A domain in Euclidean spaces is said to be pseudoconvex if exists certain kind of plurisubharmonic function. The study of global regularity of d-bar-Neumann problem on bounded pseudoconvex domains is dated back to the 1960s. However, a complete understanding of the regularity is still absent. On the other hand, the Diederich--Fornaess index was introduced in 1977 originally for seeking bounded plurisubharmonic functions. Through decades, enormous evidence has indicated a relationship between global regularity of the d-bar-Neumann problem and the Diederich--Fornaess index. Indeed, it has been a long-lasting open question whether the trivial Diederich--Fornaess index implies global regularity. In this talk, we will introduce the backgrounds and motivations. The main theorem of the talk proved recently by Emil Straube and me answers this open question for n-1 forms.