Nonlinear partial differential systems on Riemannian manifolds with their geometric applications |
| |
Authors: | Shihshu Walter Wei |
| |
Institution: | (1) Department of Mathematics, University of Oklahoma, 601 Elm Avenue, Room 423, 73019-0315 Norman, Oklahoma |
| |
Abstract: | We make the first study of how the existence of (essential) positive supersolutions of nonlinear degenerate partial differential
equations on a manifold affects the topology, geometry, and analysis of the manifold. For example, for surfaces in R3 we prove a Bernstein-type theorem that generalizes and unifies three distinct theorems. In higher dimensions, we provide
topological obstructions for a minimal hypersurface in Rn+1 to admit an essential positive supersolution. This immediately yields information about the Gauss map of complete minimal
hypersurfaces in Rn+1. By coping with a wider class of nonlinear partial differential equations that are involved with (p)-harmonic maps and (p)-superstrongly
unstable manifolds, we derive information on the regularity of minimizers, homotopy groups, and solutions to Dirichlet problems,
from the existence of essential positive supersolutions. |
| |
Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications primary 58E20 53C21 53A10 secondary 35M99 53C20 55o05 |
本文献已被 SpringerLink 等数据库收录! |
|