Theorem of Tsuji

Theorem of Tsuji

The theorem of Masatsugu Tsuji is an equivalent of the theorem of representation of Riemann in connectivity 2. It can be stated in the following way:

That is to say $K$ a related and relatively compact whole in $\backslash \; mathbb\; \{D\}$. If one notes $\backslash \; partial\; \_eK$ the border external of $K$, then the field $\backslash \; Omega$ limited by $\backslash \; partial\; \_eK$ and $\backslash \; mathbb\; \{T\}\; =\; \backslash \; partial\; \backslash \; mathbb\; \{D\}$ is in conformity with the field . Where $r\_0=caph\; (K)\; =caph\; (\backslash \; partial\; \_eK)$.

$caph\; (K)$ indicates the hyperbolic capacity of K.

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