Comparison Geometry for the Bakry-Emery Ricci Tensor
For Riemannian manifolds with a measure (M, g, e−fdvolg) we prove mean curvature and volume comparison results when the 1-Bakry-Emery Ricci tensor is bounded from below and f is bounded or Thetarf 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.
Wei, Guofang and Wylie, William, "Comparison Geometry for the Bakry-Emery Ricci Tensor" (2007). Mathematics Faculty Scholarship. 126.
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