Results 1 
2 of
2
Estimates for Conformal Capacity
, 2000
"... Let a; b; c; d be distinct points on Rn. By p we denote the minimal conformal capacity of all rings.E; F / with a; b 2 E and c; d 2 F. For n D 2, we use explicit expressions of p in terms of complete elliptic integrals to prove a sharp inequality that connects p and the conformal capacity of Teich ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Let a; b; c; d be distinct points on Rn. By p we denote the minimal conformal capacity of all rings.E; F / with a; b 2 E and c; d 2 F. For n D 2, we use explicit expressions of p in terms of complete elliptic integrals to prove a sharp inequality that connects p and the conformal capacity of Teichmüller’s ring. We also show, by a concrete example, how we can use techniques involving polarization and hyperbolic geometry to prove estimates for the conformal capacity of rings.
On the equilibrium measure and the capacity of certain condensers
 Illinois J. Math
"... mass, harmonic measure. We prove some geometric estimates for the equilibrium measure and the capacity of certain condensers. The proofs are based on the interpretation of the equilibrium measure as the distributional Laplacian of the corresponding potential, on a formula of T.Bagby, and on a metho ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
mass, harmonic measure. We prove some geometric estimates for the equilibrium measure and the capacity of certain condensers. The proofs are based on the interpretation of the equilibrium measure as the distributional Laplacian of the corresponding potential, on a formula of T.Bagby, and on a method of Beurling and Nevanlinna that involves the transport of the Riesz mass of a superharmonic function. 1