Prescribing the symmetric function of the eigenvalues of the Schouten tensor

2010/10/29 by Yan He, Weimin Sheng, He, Yan +1
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1010.6116

Abstract

In this paper we study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Schouten tensor on compact Riemannian manifolds with boundary. We prove its solvability and the compactness of the solution set, provided the Ricci tensor is non-negative definite.

Related

• Schouten tensor equations in conformal geometry with prescribed boundary metric
• Poincare-Einstein metrics and the Schouten tensor
• Rigidity of Schouten Tensor under Conformal Deformation
• An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature
• Conformal deformations of the smallest eigenvalue of the Ricci tensor