Dirichlet Problems for Plurisubharmonic Functions on Compact Sets
Evgeny A. Poletsky, Ragnar Sigurdsson
TL;DR
This paper addresses the solution of Dirichlet problems for various classes of plurisubharmonic functions on compact sets in complex space, expanding the understanding of boundary value problems in pluripotential theory.
Contribution
It introduces methods to solve Dirichlet problems for continuous, pluriharmonic, and maximal plurisubharmonic functions on compact sets in ^n, broadening existing theoretical frameworks.
Findings
Established existence of solutions for Dirichlet problems in specified classes
Extended pluripotential theory to compact sets in ^n
Provided new techniques for boundary value problems in complex analysis
Abstract
In this paper we solve the Dirichlet problems for different classes of plurisubharmonic functions on compact sets in including continuous, pluriharmonic and maximal functions.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Geometry and complex manifolds