Area growth rate of the level surface of the potential function on the 3-dimensional steady gradient Ricci soliton

Guo, Hongxin

doi:10.1090/S0002-9939-09-09792-5

Area growth rate of the level surface of the potential function on the 3-dimensional steady gradient Ricci soliton
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Proc. Amer. Math. Soc. 137 (2009), 2093-2097 Request permission

Abstract:

In this short note we show that on a 3-dimensional steady gradient Ricci soliton with positive curvature and which is $\kappa$-noncollapsed on all scales, the scalar curvature and the mean curvature of the level surface of the potential function both decay linearly. Consequently we prove that the area of the level surface grows linearly.

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