The Grushin hemisphere as a Ricci limit space with curvature ≥1

Proceedings of the American Mathematical Society, Series B Pub Date : 2023-03-24 DOI:10.1090/bproc/160

Jiayin Pan

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引用次数: 3

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 S^{m+n} with R i c ≥ 1 Ric\ge 1 such that its Gromov-Hausdorff limit is the n n -dimensional Grushin hemisphere.