The volume growth of complete gradient shrinking Ricci solitons

Abstract

We prove that any gradient shrinking Ricci soliton has at most Euclidean volume growth. This improves a recent result of H.-D. Cao and D. Zhou by removing a condition on the growth of scalar curvature.

References in corpus (2)

• Ricci flow with surgery on three-manifolds
• On complete gradient shrinking Ricci solitons

Cited by in corpus (8)

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• Sharp logarithmic Sobolev inequalities on gradient solitons and applications
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• Time analyticity for heat equation on gradient shrinking Ricci solitons
• A necessary and sufficient condition for Ricci shrinkers to have positive AVR
• Harmonic and Schrödinger functions of polynomial growth on gradient shrinking Ricci solitons
• A compactness theorem for four-dimensional shrinking gradient Ricci solitons
• Volume estimates and the asymptotic behavior of expanding gradient Ricci solitons