Supports of Weighted Equilibrium Measures and Examples
Muhammed Al\.i Alan
TL;DR
This paper explores the supports of weighted equilibrium measures in complex spaces, providing explicit examples, new plurisubharmonic function constructions, and discussing open problems related to Monge-Ampère equations.
Contribution
It introduces explicit examples of supports for weighted equilibrium measures and new methods for constructing plurisubharmonic functions in the Lelong class.
Findings
Explicit examples of supports for weighted equilibrium measures.
New constructions of plurisubharmonic functions in the Lelong class.
Open problems related to Monge-Ampère equations and extremal measures.
Abstract
We analyze the supports of weighted equilibrium measures in . We give explicit examples of families of compact sets which arise as the support of a weighted equilibrium measure for some admissible weight . These examples also give new constructions of plurisubharmonic functions in the Lelong class. We also include a list of open problems on the support of extremal measures which are related to solutions of Monge-{A}mp\`ere equations.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Algebra and Geometry