Harmonic measure

can any person will certainly aid me to do this troubles:

  1. Let $\mathcal D$ be the device disk a Set $E\subseteq\partial\mathcal D$ has harmonic action identically $0$ relative to $\mathcal D$. What can you end concerning $E$?
  2. Allow $\Omega\subseteq\mathbb C$ be a domain name and also allow $E \text{ and } E'\subseteq\Omega$ such that $\omega(z,\Omega,E)\ge\omega(z,\Omega,E') \forall z\in\Omega$. What can you end concerning $E$ and also $E'$?

Troubles are extracted from Respected Stephen Krantz is Geometric function concept publication chapter9.

2022-06-07 14:35:39
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