Invariant proper holomorphic maps between balls

We consider proper holomorphic maps between balls that are invariant under the action of finite groups of unitary matrices. We are primarily interested in actions of groups that are fixed-point-free; for purposes of comparison we will briefly consider matrix groups that act with fixed points (that is, groups that have at least one nontrivial element with an eigenvalue of one) in the last chapter. Forstneric showed that given any finite unitary fixed-point-free matrix group, there exists a proper holomorphic map from the ball in the appropriate dimensional complex Euclidean space to a higher dimensional ball, that is invariant under the action of that group. He showed on the other hand that if we also require the map to be smooth to the boundary, then many groups are ruled out.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Lichtblau, Daniel

Contributors dc:contributor

• D'Angelo, John P.

• Mathematics

Statement dc:rights

• Copyright 1991 Lichtblau, Daniel

Language dc:language

eng

Identifier

AAI9210893
(UMI)AAI9210893

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23603