Calabi-Yau type theorem for complete manifolds with nonnegative scalar curvature

Jintian Zhu

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arXiv · 2402.15118

Calabi-Yau type theorem for complete manifolds with nonnegative scalar curvature

Jintian Zhu

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Abstract

In this paper, we are able to prove an analogy of the Calabi-Yau theorem for complete Riemannian manifolds with nonnegative scalar curvature which are aspherical at infinity. The key tool is an existence result for arbitrarily large bounded regions with weakly mean-concave boundary in Riemannian manifolds with sublinear volume growth. As an application, we use the same tool to show that a complete contractible Riemannian $3$-manifold with positive scalar curvature and sublinear volume growth is necessarily homeomorphic to $\mathbb R^3$.

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Jintian Zhu. 2024-02-23. Calabi-Yau type theorem for complete manifolds with nonnegative scalar curvature. https://arxiv.org/abs/2402.15118

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