Interpolation of Weighted L2 Holomorphic Functions in Higher Dimensions

This thesis considers an interpolation theorem in the setting of several complex variables. We consider a Kahler manifold X with a metric &ohgr; whose Ricci curvature is non-positive and we assume that X admits a Green's function. In this setup we give a sufficient condition for a closed smooth uniformly flat hypersurface W in X to be interpolating. Our condition is expressed in terms of a geometric density of the hypersurface which generalizes the density notion used for hypersurfaces in the Bergman ball and in n-dimensional Euclidean space.

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

2015

Author dc:creator

• Forgacs, Tamas

Contributors dc:contributor

• Dror Varolin

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3290235

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86882