All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 141

Showing per page

Determination of the pluripolar hull of graphs of certain holomorphic functions

Armen Edigarian, Jan Wiegerinck (2004)

Annales de l’institut Fourier

Let A be a closed polar subset of a domain D in ℂ . We give a complete description of the pluripolar hull Γ D × ℂ * of the graph Γ of a holomorphic function defined on D ∖ A . To achieve this, we prove for pluriharmonic measure certain semi-continuity properties and a localization principle.

Dichotomy of global density of Riesz capacity

Hiroaki Aikawa (2016)

Studia Mathematica

Let C α be the Riesz capacity of order α, 0 < α < n, in ℝⁿ. We consider the Riesz capacity density ̲ ( C α , E , r ) = i n f x ∈ ℝ ⁿ C α ( E ∩ B ( x , r ) ) / C α ( B ( x , r ) ) for a Borel set E ⊂ ℝⁿ, where B(x,r) stands for the open ball with center at x and radius r. In case 0 < α ≤ 2, we show that l i m r → ∞ ̲ ( C α , E , r ) is either 0 or 1; the first case occurs if and only if ̲ ( C α , E , r ) is identically zero for all r > 0. Moreover, it is shown that the densities with respect to more general open sets enjoy the same dichotomy. A decay estimate for α-capacitary potentials is also obtained.

Equality cases for condenser capacity inequalities under symmetrization

Dimitrios Betsakos, Stamatis Pouliasis (2012)

Annales UMCS, Mathematica

It is well known that certain transformations decrease the capacity of a condenser. We prove equality statements for the condenser capacity inequalities under symmetrization and polarization without connectivity restrictions on the condenser and without regularity assumptions on the boundary of the condenser.

Currently displaying 21 – 40 of 141