2020/04/29 by Cheng, Xu, Ribeiro, Ernani, Zhou, Detang · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2004.14426
In this article, we provide some volume growth estimates for complete noncompact gradient Ricci solitons and quasi-Einstein manifolds similar to the classical results by Bishop, Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. We prove a sharp volume growth estimate for complete noncompact gradient shrinking Ricci soliton. Moreover, we provide upper bound volume growth estimates for complete noncompact quasi-Einstein manifolds with λ=0. In addition, we prove that geodesic balls of complete noncompact quasi-Einstein manifolds with λ<0 and μ≤ 0 have at most exponential volume growth.