Willhelm Stoll will continue his investigations of the value distribution theory of meromorphic maps for fixed and moving targets and the geometry and analysis of parabolic spaces. In particular he will work on conjectures of Nevanlinna, Griffiths and Cartan as well as on the interpretation of the curvature stress formula, algebroid reduction and the Ricci function on parabolic manifolds. Pit-Mann Wong will investigate the singularities of solutions to the complex homogeneous Monge-Ampere equation. In particular he will study the relationship between the singular set and totally real embedding. He will also study Nevanlinna theory from the point of view of complex affine geometry. The problems to be addressed by Stoll are all important in value distribution theory of several variables. The problem of moving targets involves the question of how often the image of the map agrees with the image of some given map of slower growth. The Cartan conjecture involves allowing degeneracy of the map. The Griffiths conjecture is concerned with non-equidimensional value distribution theory. Together with Wong he will investigate problems arising from the fact that complex Euclidean space can be characterized by the existence of an exhaustion function satisfying a homogeneous complex Monge-Ampere equation.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
8702144
Program Officer
James Glazebrook
Project Start
Project End
Budget Start
1987-07-01
Budget End
1990-12-31
Support Year
Fiscal Year
1987
Total Cost
$179,412
Indirect Cost
Name
University of Notre Dame
Department
Type
DUNS #
City
Notre Dame
State
IN
Country
United States
Zip Code
46556