Comparison geometry for the Bakry-Emery Ricci tensor
Comparison geometry for the Bakry-Emery Ricci tensor
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DOI：
10.4310/jdg/1261495336
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发表时间：
2007-06
影响因子：
2.5
通讯作者：
Guofang Wei;W. Wylie
中科院分区：
文献类型：
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作者：
Guofang Wei;W. Wylie
对于具有测度(M，g，edvolg)的黎曼流形，我们证明了当∞-Bakry-Emery Ricci张量从下有界且f有界或∂Rf从下有界时的平均曲率和体积比较结果，推广了经典的结果(即当f为常数时)。这导致了许多关于Ricci曲率的定理被推广到Bakry-Emery Ricci张量以下。特别地，我们给出了当f有界时所有主要比较定理的推广。简单的例子表明，f上的界是这些结果所必需的。
For Riemannian manifolds with a measure (M, g, edvolg) we prove mean curvature and volume comparison results when the ∞-Bakry-Emery Ricci tensor is bounded from below and f is bounded or ∂rf is bounded from below, generalizing the classical ones (i.e. when f is constant). This leads to extensions of many theorems for Ricci curvature bounded below to the Bakry-Emery Ricci tensor. In particular, we give extensions of all of the major comparison theorems when f is bounded. Simple examples show the bound on f is necessary for these results.