Convergence in capacity of plurisubharmonic functions with given boundary values
Nguyen Xuan Hong, Nguyen Van Trao, Tran Van Thuy
TL;DR
This paper investigates how sequences of plurisubharmonic functions converge in capacity and applies these results to demonstrate stability in solutions of complex Monge-Ampère equations.
Contribution
It establishes new convergence results in capacity for plurisubharmonic functions and proves stability of solutions to complex Monge-Ampère equations.
Findings
Convergence in capacity is characterized for sequences of plurisubharmonic functions.
Stability results for solutions of complex Monge-Ampère equations are proved.
Applications to boundary value problems in complex analysis.
Abstract
In this paper, we study the convergence in the capacity of sequence of plurisubharmonic functions. As an application, we prove stability results for solutions of the complex Monge-Amp\`ere equations.
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