2006/08/20 by Behroz Bidabad, Bidabad, Behroz, S. Hedayatian +2
Mathematics · #30C70 #53A30 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #math.DG #math.MG #msc:30C70 #msc:53A30
paper · pdf · doi:10.48550/arxiv.math/0608494
The Fifth Conference of Balkan Society of Geometers, August 29 - September 2, 2005, Mangalia-Romania, pp. 34-43
arxiv created 2006/08/20 · openalex publication_date 2006/08/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The electric capacity of a conductor in the 3-dimensional Euclidean space R3 is defined as a ratio of a given positive charge on the conductor to the value of potential on the surface. This definition of the capacity is independent of the given charge. The capacity of a set as a mathematical notion was defined first by N. Wiener (1924) and was developed by O. Forstman, C. J. de La Vallee Poussin, and several other French mathematicians in connection with potential theory. This paper develops the theory of conformal invariants for Finsler manifolds. More precisely we prove: The capacity of a compact set and the capacity of the condenser of two closed sets are conformally invariant. By mean of the notion of capacity, we construct and study four conformal invariant functions ρ, ν, μ and λ which have similarities with the classical invariants on Sn, Rn or Hn. Their properties and especially their continuity are efficient tools for solving some problems of conformal geometry in the large.