Preprint

Inserted: 9 jan 2025
Last Updated: 9 jan 2025

Year: 2025
Notes:

Comments are welcome!

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.

Keywords: Ricci curvature, RCD spaces, Gromov-Hausdorff

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• Survey_Varenna.pdf