论文标题
梯度缩小的Ricci孤子子的几何不平等和刚性
Geometric inequalities and rigidity of gradient shrinking Ricci solitons
论文作者
论文摘要
在本文中，我们证明了Sobolev不平等，对数Sobolev不平等，Schrödinger热核上限，Faber-Krahn不平等，NASH不平等和Rozenblum-Cwikel-Lieb不平等，所有这些都在完全的ninkegrient nightegrient nightegrient nightegn nighent ninkci selinkci soliton上存在。我们还获得了一些积分差距定理，用于紧凑的缩小ricci孤子。
In this paper we prove that the Sobolev inequality, the logarithmic Sobolev inequality, the Schrödinger heat kernel upper bound, the Faber-Krahn inequality, the Nash inequality and the Rozenblum-Cwikel-Lieb inequality all equivalently exist on complete gradient shrinking Ricci solitons. We also obtain some integral gap theorems for compact shrinking Ricci solitons.
