CoSy Seminar: The Diederich–Fornæss index and the ¯∂-Neumann problem

Anyone is welcome to join in and the first 40 people to register will be treated to a free lunch sandwich. If you do not want lunch, you are still free to attend without registrating. 

Register for a free lunch sandwich (deadline: 26 November).

Abstract: A domain Ω ⊂ C n is said to be pseudoconvex if − log(−δ(z)) is plurisubharmonic in Ω, where δ is a signed distance function of Ω. The study of global regularity of ¯∂-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–Fornæss index was introduced in 1977 originally for seeking bounded plurisubharmonic functions. Through decades, enormous evidence has indicated a relationship between global regularity of the ¯∂-Neumann problem and the Diederich–Fornæss index. Indeed, it has been a long-lasting open question whether the trivial Diederich–Fornæss 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 (0, n − 1) forms.

This is a lecture in the seminar series given by CIM (Centre for Interdisciplinary Mathematics).