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arXiv · 2510.17536

The existence of negatively curved metrics on locally conformally flat manifolds with boundary

Rirong Yuan
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Abstract

We use certain Morse functions to construct conformal metrics with negative sectional curvature on locally conformally flat manifolds with boundary. Moreover, without conformally flatness assumption, we also construct conformal metric of positive Einstein tensor.

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Rirong Yuan. 2025-10-20. The existence of negatively curved metrics on locally conformally flat manifolds with boundary. https://arxiv.org/abs/2510.17536

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