Schouten tensor equations in conformal geometry with prescribed boundary metric

Date

2005-07-15

Authors

Schnurer, Oliver C.

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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.

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Attribution 4.0 International

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