Finite Pluricomplex energy measures
Eleonora Di Nezza
TL;DR
This paper studies probability measures with finite pluricomplex energy, providing criteria for finiteness, testing examples, and exploring invariance properties under biholomorphic and bimeromorphic transformations.
Contribution
It introduces criteria for finite pluricomplex energy measures and analyzes their invariance properties, advancing understanding in pluripotential theory.
Findings
Criteria for finite pluricomplex energy measures
Examples illustrating the criteria
Finite energy is biholomorphic invariant but not bimeromorphic
Abstract
We investigate probability measures with finite pluricomplex energy. We give criteria insuring that a given measure has finite energy and test these on various examples. We show that this notion is a biholomorphic but not a bimeromorphic invariant.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Algebra and Geometry