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2009

On complete gradient shrinking Ricci solitons

Cao, Huai-Dong, Zhou, Detang

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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.

On complete gradient shrinking Ricci solitons · Around

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Schoen, R. and Yau, S.-T., Lectures on Differential Geometry
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Hamilton, R. S., The formation of singularities in the Ricci flow
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Feldman, M., Ilmanen, T. and Knopf, D., Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons , J. Differential Geom., 65
2003
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Morgan, F., Manifolds with density
2005
Earlier work this paper cites.

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Then

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