论文标题
RICCI孤子和准元素歧管的体积增长估计值
Volume growth estimates for Ricci solitons and quasi-Einstein manifolds
论文作者
论文摘要
在本文中，我们提供了一些与Bishop，Calabi和Yau的经典结果相似的完整非相关梯度RICCI孤子和准伊因斯坦歧管的体积增长估计值。我们证明，对于完全非紧密梯度缩小的Ricci Soliton，我们证明了急剧的增长估计值。此外，我们为$λ= 0提供了完整的非脉冲准元素歧管的上限量增长估计值。此外，我们证明，具有$λ<0 $和$μ\ leq 0 $的完整非稳定准元素歧管的地理球具有最大的指数增长。
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 $μ\leq 0$ have at most exponential volume growth.
