Colloquium Mathematics, Prof.dr. J. Wiegerinck (UvA)

Join us for coffee and tea at 15.30 p.m.

Date:                         Tuesday, December 10^th 2013
Speaker:                    Prof. J. Wiegerinck (KdV Institute for Mathematics, UvA)
Room:                        5161.0293 (Bernoulliborg)
Time:                         16.30

Title: Plurifine Potential Theory

Abstract:

The fine topology is the weakest topology on domains in R^n that makes all subharmonic functions continuous. It allows to introduce finely subharmonic --- and in the 2-dimensional
case also finely holomorphic --- functions in a natural way. These are functions that satisfy the
analogue of the mean value property and of the Cauchy-Riemann equations in the fine setting.

In C^n the plurifine topology, which makes all plurisubharmonic functions continuous, is challenging. In this setting we introduced a weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions. Strong will imply weak, but it is
unknown whether the two concepts are the same.

However, we will start by discussing motivation for this kind of generalizations. Some phenomena in classical complex analysis make it natural to study these plurifinely functions. Next we present some of our work on plurifinely plurisubharmonic and holomorphic functions.

(All this is joint work, partly with Said El Marzguioui, and partly with Mohamed El Kadiri and Bent Fuglede.)

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and

Dr. A.V. Kiselev (e-mail: a.v.kiselev rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/