Harmonic measure and conformal length

Øyma, Knut

doi:10.1090/S0002-9939-1992-1101991-1

Harmonic measure and conformal length
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by Knut Øyma

Proc. Amer. Math. Soc. 115 (1992), 687-689

DOI: https://doi.org/10.1090/S0002-9939-1992-1101991-1

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Abstract:

Let $f(z)$ be any univalent function that maps the unit disc onto a domain $\Omega$. We prove that for any line $L$ the length of ${f^{ - 1}}(\Omega \cap L)$ is less than $4\pi$.

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