Interior estimates for $p$-plurisubharmonic functions
Slawomir Dinew
TL;DR
This paper establishes interior estimates for solutions to a Monge-Ampère type equation within the class of p-plurisubharmonic functions, leading to classification results for functions with constant operator and quadratic growth.
Contribution
It provides the first and second order interior estimates for p-plurisubharmonic functions solving a Monge-Ampère type equation, and characterizes quadratic solutions with constant operator.
Findings
Interior estimates for p-plurisubharmonic functions
Classification of quadratic solutions with constant operator
Solutions with quadratic growth are quadratic polynomials
Abstract
We study a Monge-Amp\`ere type equation in the class of -plurisubharmonic functions and establish first and second order interior estimates. As an application of these we show that -plurisubharmonic functions with constant operator and quadratic growth must be quadratic polynomials.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Mathematical Physics Problems