Let be the open unit disc. A non-constant holomorphic mapping is called an analytic disc in . The really refers to both the embedding and the image. If the mapping extends continuously to the closed unit disc , then is called a closed analytic disc and is called the boundary of a closed analytic disc.
Another use of analytic discs are as a technique for extending CR functions on generic manifolds . The idea here is that you can always extend a function from the boundary of a disc to the inside of the disc by solving the Dirichlet problem.
A closed analytic disc is said to be attached to a set if , that is if maps the boundary of the unit disc to .
Analytic discs are also used for defining the Kobayashi metric and thus plays a role in the study of invariant metrics.
- 1 M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. , Princeton University Press, Princeton, New Jersey, 1999.
- 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
|Date of creation||2013-03-22 14:30:49|
|Last modified on||2013-03-22 14:30:49|
|Last modified by||jirka (4157)|
|Defines||closed analytic disc|
|Defines||boundary of a closed analytic disc|
|Defines||attached analytic disc|