Continuity of plurisubharmonic envelopes
Date of Award
Doctor of Philosophy (PhD)
Continuity, Plurisubharmonic envelopes, Jensen measures
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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Gogus, Nihat Gokhan, "Continuity of plurisubharmonic envelopes" (2006). Mathematics - Dissertations. Paper 23.