A Bakry–Émery Almost Splitting Result With Applications to the Topology of Black Holes

  title={A Bakry–{\'E}mery Almost Splitting Result With Applications to the Topology of Black Holes},
  author={Gregory J. Galloway and Marcus A. Khuri and Eric Woolgar},
  journal={arXiv: Differential Geometry},
The almost splitting theorem of Cheeger-Colding is established in the setting of almost nonnegative generalized $m$-Bakry-Emery Ricci curvature, in which $m$ is positive and the associated vector field is not necessarily required to be the gradient of a function. In this context it is shown that with a diameter upper bound and volume lower bound the fundamental group of such manifolds is almost abelian. Furthermore, extensions of well-known results concerning Ricci curvature lower bounds are… Expand
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  • F. Wang, Xiaohua Zhu
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
  • 2019
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