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arXiv · 2501.07125

The large scale structure of complete $4$-manifolds with nonnegative Ricci curvature and Euclidean volume growth

Daniele Semola
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Abstract

We survey the implications of our joint work with E. Bru\`e and A. Pigati on the structure of blow-downs for a smooth, complete, Riemannian $4$-manifold with nonnegative Ricci curvature and Euclidean volume growth. Very imprecisely, any such manifold looks like a cone over a spherical space form at infinity. We present some open questions and discuss possible future directions along the way.

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Daniele Semola. 2025-01-13. The large scale structure of complete $4$-manifolds with nonnegative Ricci curvature and Euclidean volume growth. https://doi.org/10.1016/j.indag.2025.04.003

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