Notes on Conformal Metrics of Negative Curvature on Manifolds with Boundary

Abstract

We use certain Morse functions to construct conformal metrics such that the eigenvalue vector of modified Schouten tensor belongs to a given cone. As a result, we prove that any Riemannian metric on compact 3-manifolds with boundary is confor-mal to a compact metric of negative sectional curvature.

Keywords

Schouten tensor / Modified Schouten tensor / conformal deformation / Morse theory