Geodesic
Hülder Conditions and the Topology of Simply Connected Domains*
Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 189-191

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DOI

Let ƒ be regular univalent and normalized in the unit disc U (i.e. ƒ ∊ S) and continuous on U ∈ T, where T denotes the boundary of U.Recently Essén proved [5] a conjecture of Piranian [7] stating that if the derivative of ƒ ∊ S is bounded in U and ƒ(z1) = ƒ(z2) = ... = ƒ(z n ) for Z j ∊ T, 1 ≤ j ≤ n, then n ≤ 2. In fact, Essén proved a more general result, using a deep result on harmonic functions. The aim of the following article is to replace Essén's proof by a completely different proof which is based only on Goluzin's inequalities and is much more elementary.
DOI : 10.4153/CMB-1983-030-1
Mots-clés : 30C55 
Aharonov, Dov. Hülder Conditions and the Topology of Simply Connected Domains*. Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 189-191. doi: 10.4153/CMB-1983-030-1
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     title = {H\"ulder {Conditions} and the {Topology} of {Simply} {Connected} {Domains*}},
     journal = {Canadian mathematical bulletin},
     pages = {189--191},
     year = {1983},
     volume = {26},
     number = {2},
     doi = {10.4153/CMB-1983-030-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-030-1/}
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