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Bloch's theorem (Theorem)

Let $ f$ be an holomorphic function on a region containing the closure of the disk $ D=\{z\in\mathbb{C}:\vert z\vert<1\}$, such that $ f(0)=0$ and $ f'(0)=1$. Then there is a disk $ S\subset D$ such that $ f$ is injective on $ S$ and $ f(S)$ contains a disk of radius $ \frac{1}{72}$.



"Bloch's theorem" is owned by Koro.
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Bloch's constant (Definition) by alozano
Landau's constant (Definition) by alozano
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Cross-references: radius, contains, injective, closure, region, holomorphic function
There are 3 references to this entry.

This is version 2 of Bloch's theorem, born on 2002-12-11, modified 2002-12-11.
Object id is 3733, canonical name is BlochsTheorem.
Accessed 8851 times total.

Classification:
AMS MSC: 32H02 (Several complex variables and analytic spaces :: Holomorphic mappings and correspondences :: Holomorphic mappings, embeddings and related questions)
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Discussion
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Settled oneself! by aragon on 2007-02-14 09:30:15
One should read always first the operating instruction.
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Why should the theorem be unproven? by aragon on 2007-02-14 09:23:31
I do not understand, why the theorem is as as unproven tagged. André Bloch supplied the proof.

Show here:
http://de.wikipedia.org/wiki/Satz_von_Bloch
[ reply | up ]
1/72 in Bloch's theorem by PrimeFan on 2006-11-10 16:48:24
I'm curious about this 1/72 in this article on Bloch's theorem that is currently tagged as "unproven." (If it weren't for that literal, I wouldn't care less about it).

I thought maybe Wikipedia might say something about it, but apparently in physics there is something else called Bloch's theorem, which has to do with a model of particle physics known as Bloch waves. This was studied by Felix Bloch, who from the WP article about him one might deduce he didn't much care about math not applicable to physics.

Next I thought of looking at Mathworld (please put away the garlic and crosses). The MW article on topology cites a book by E. Bloch, A First Course in Geometric Topology and Differential Geometry. This E. Bloch is probably neither the composer Ernest Bloch nor the Marxist philosopher Ernst Bloch.

In short, this entry raises a lot of questions besides how to prove Bloch's theorem.
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