Notes on conformal metrics of negative curvature on manifolds with boundary

Rirong Yuan

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arXiv · 2308.05979

Notes on conformal metrics of negative curvature on manifolds with boundary

Rirong Yuan

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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 conformal to a compact metric of negative sectional curvature.

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Rirong Yuan. 2023-08-11. Notes on conformal metrics of negative curvature on manifolds with boundary. https://arxiv.org/abs/2308.05979

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