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Comparison geometry for the bakry-emery ricci tensor. Arxiv:math.dg /0706.1120.
| Content Provider | CiteSeerX |
|---|---|
| Author | Wei, Guofang Wylie, Will |
| Abstract | For Riemannian manifolds with a measure (M, g,e −f dvolg) 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). As application we extend many results for Ricci curvature lower bound to Bakry-Emery Ricci tensor bounded below. In particular, we show that the Cheeger-Gromoll splitting theorem holds if the Bakry-Emery Ricci tensor is nonnegative and f is bounded and thus the fundamental group of a compact manifold M n with nonnegative Bakry-Emery Ricci tensor is abelian up to finite index with rank less or equal to n. 1 |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Bakry-emery Ricci Tensor Comparison Geometry Riemannian Manifold Classical One Compact Manifold Nonnegative Bakry-emery Ricci Tensor Volume Comparison Result Ricci Curvature Many Result Cheeger-gromoll Splitting Theorem Mean Curvature Fundamental Group |
| Content Type | Text |
