Abstract:
We obtain upper bounds for the conformal modulus of a condenser with uniformly perfect plates and for the reduced modulus of a uniformly perfect set $E$ at $a\in\overline{\mathbb R}^n\setminus E$. For the reduced moduli of $\alpha$-uniformly perfect sets we prove the continuity property with respect to the kernel convergence of the complements to these sets in the sense of Carathéodory.
Keywords:conformal capacity, reduced modulus, kernel convergence, filling of sets.
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