Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary

Jingche Chen; Han Hong

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arXiv · 2510.13099

Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary

Jingche Chen·Han Hong

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Abstract

We establish curvature obstruction theorems for manifolds with boundary. Our main theorems show that, for dimensions up to 7, a topologically nontrivial compact manifold with boundary cannot have a metric of positive $m$-intermediate curvature if the boundary is $m$-convex, and some rigidity result holds if $m$-intermediate curvature is nonnegative. This non-existence persists after performing a connected sum with an arbitrary manifold. These results generalize results of \cite{brendle,chenshuli,ChuKwongLee,Xu} to manifold with boundary.

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Jingche Chen, Han Hong. 2025-10-15. Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary. https://arxiv.org/abs/2510.13099

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