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| 1 | Polygon |
| 1 | Closed Operator |
| 1 | Strict |
| 1 | Superset |
| 1 | Injective Function |
| 1 | Relation Theory |
| 1 | Number |
| 2 | Radius |
| 2 | Holomorphic |
| 3 | Supremum |
| 20 | Blochs Constant |
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Landaus Constant
We suggest that the reader reads first the entry on Bloch's constant. Let
be the set of all functions
holomorphic
on a region
containing the
closure
of the disk
and satisfying
and 
. For each
let
be the supremum
of all numbers
such that there is a disk
such that 
contains
a disk of radius
(notice that here we don't require 
to be injective
on 
).
is defined by
Let 
be Bloch's constant. Then, clearly, 
. The exact value of 
(as that of 
) is not known but it has been shown that
. In particular, it is known that 
is strictly
greater than 
.
Bibliography
-
- 1
- John B. Conway, Functions of One Complex
Variable I, Second Edition, 1978, Springer-Verlag, New York.