Title

Continuity of plurisubharmonic envelopes

Date of Award

8-2006

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Advisor(s)

Evgeny Poletsky

Keywords

Continuity, Plurisubharmonic envelopes, Jensen measures

Subject Categories

Mathematics

Abstract

Let D be a domain in [Special characters omitted.] . The plurisubharmonic envelope of a function [varphi] [is an element of] C(D¯) is the supremum of all plurisubharmonic functions which are not greater than [varphi] on D . A bounded domain D is called c-regular if the envelope of every function [varphi] [is an element of] C(D¯) is continuous on D and extends continuously to D¯ . The purpose of this thesis is to give a complete characterization of c -regular domains in terms of Jensen measures . We show using Gauthier's Fusion Lemma that a domain is locally c -regular if and only if it is c -regular.

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