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arXiv · 2012.11677

Manifolds with positive curvature operator and strictly convex bounday

Yongjia Zhang
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Abstract

In [AMW], it is proved that if a compact $3$-manifold has positive Ricci curvature and strictly convex boundary, then this manifold is diffeomorphic to the standard $3$-dimensional Euclidean disk. In this paper, we prove its higher-dimensional generalization: if a compact $n$-manifold has positive curvature operator and strictly convex boundary, then this manifold is diffeomorphic to the standard $n$-dimensional Euclidean disk.

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Yongjia Zhang. 2020-12-21. Manifolds with positive curvature operator and strictly convex bounday. https://arxiv.org/abs/2012.11677

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