The Grushin hemisphere as a Ricci limit space with curvature $\ge 1$

Abstract

The Grushin sphere is an almost-Riemannian manifold that degenerates along its equator. We construct a sequence of Riemannian metrics on a sphere $S^{m+n}$ with $Ric\ge 1$ such that its Gromov-Hausdorff limit is the $n$-dimensional Grushin hemisphere.

Slightly changed some wordings in the introduction

References in corpus (1)

• Examples of Ricci limit spaces with non-integer Hausdorff dimension

Cited by in corpus (2)

• Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries
• Singular Weyl's law with Ricci curvature bounded below