Schouten tensor equations in conformal geometry with prescribed boundary metric
Date
2005-07-15
Authors
Schnurer, Oliver C.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We deform the metric conformally on a manifold with boundary. This induces a deformation of the Schouten tensor. We fix the metric at the boundary and realize a prescribed value for the product of the eigenvalues of the Schouten tensor in the interior, provided that there exists a subsolution. This problem reduces to a Monge-Ampere equation with gradient terms. The main issue is to obtain a priori estimates for the second derivatives near the boundary.
Description
Keywords
Schouten tensor, Fully nonlinear equation, Conformal geometry, Dirichlet boundary value problem
Citation
Schnürer, O. C. (2005). Schouten tensor equations in conformal geometry with prescribed boundary metric. <i>Electronic Journal of Differential Equations, 2005</i>(81), pp. 1-17.
Rights
Attribution 4.0 International