On complete gradient shrinking Ricci solitons

Abstract

In this paper we derive a precise estimate on the growth of potential functions of complete noncompact shrinking solitons. Based on this, we prove that a complete noncompact gradient shrinking Ricci soliton has at most Euclidean volume growth. The latter result can be viewed as an analog of the well-known theorem of Bishop that a complete noncompact Riemannian manifold with nonnegative Ricci curvature has at most Euclidean volume growth.

Theorem 1.2 improved; Corollary 1.1 added

References in corpus (1)

• Geometry of Complete Gradient Shrinking Ricci Solitons

Cited by in corpus (5)

• A compactness theorem for complete Ricci shrinkers
• Geometry of Complete Gradient Shrinking Ricci Solitons
• The volume growth of complete gradient shrinking Ricci solitons
• Remarks on non-compact gradient Ricci solitons
• The Curvature of Gradient Ricci Solitons