A comparison principle for Bergman kernels
Bo Berndtsson
TL;DR
This paper introduces a comparison principle replacing the Monge-Ampère measure with the Bergman kernel in pluripotential theory, leading to a new maximum principle.
Contribution
It presents a novel comparison principle involving Bergman kernels, extending classical pluripotential theory methods.
Findings
Establishes a new comparison principle for Bergman kernels.
Derives a maximum principle from the comparison principle.
Abstract
We give a version of the comparison principle from pluripotential theory where the Monge-Amp\`ere measure is replaced by the Bergman kernel and use it to derive a maximum principle
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Holomorphic and Operator Theory