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Invariance of Green equilibrium measure on the domain

2011/01/14 by Stamatis Pouliasis, Pouliasis, Stamatis
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Partial Differential Equations #math.CV

paper · pdf · doi:10.48550/arxiv.1101.2873

9 pages

arxiv created 2011/01/14 · openalex publication_date 2011/01/14 · arxiv updated 2011/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Green equilibrium measure and the Green equilibrium energy of a compact set K relative to the domains D and G are the same if and only if D is nearly equal to G, for a wide class of compact sets K. Also, we prove that equality of Green equilibrium measures arises if and only if the one domain is related with a level set of the Green equilibrium potential of K relative to the other domain.

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