A necessary and sufficient condition for Ricci shrinkers to have positive AVR

Details A necessary and sufficient condition for Ricci shrinkers to have positive AVR A necessary and sufficient condition for Ricci shrinkers to have positive AVR

2011-01-18

arxiv.org/abs/1101.3563v1

Mathematics

Differential Geometry

3 pages

Scientific paper

In this short note we observe that a recent result of C.-W. Chen meshes well
with earlier work of H.-D. Cao and D.-T. Zhou, O. Munteanu, J. Carrillo and L.
Ni, and S.-J. Zhang to give a necessary and sufficient condition for complete
noncompact shrinking gradient Ricci solitons to have positive asymptotic volume
ratio.

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