The nonuniqueness of the tangent cones at infinity of Ricci-flat manifolds

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Abstract

Colding and Minicozzi established the uniqueness of the tangent cones at infinity of Ricci-flat manifolds with Euclidean volume growth where at least one tangent cone at infinity has a smooth cross section. In this paper, we raise an example of a Ricci-flat manifold implying that the assumption for the volume growth in the above result is essential. More precisely, we construct a complete Ricci-flat manifold of dimension 4 with non-Euclidean volume growth that has infinitely many tangent cones at infinity where one of them has a smooth cross section.

Original languageEnglish
Pages (from-to)2683-2723
Number of pages41
JournalGeometry and Topology
Volume21
Issue number5
DOIs
Publication statusPublished - 2017 Aug 15

ASJC Scopus subject areas

  • Geometry and Topology

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