171 research outputs found
Comparison Geometry for the Bakry-Emery Ricci Tensor
For Riemannian manifolds with a measure we prove mean
curvature and volume comparison results when the -Bakry-Emery Ricci
tensor is bounded from below and is bounded or is bounded
from below, generalizing the classical ones (i.e. when 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 is bounded. Simple examples show the bound on
is necessary for these results.Comment: 21 pages, Some of the estimates have been improved. In light of some
new references, and to improve the exposition, the paper has been
reorganized. An appendix is also adde
Hitchin-Thorpe Inequality for Noncompact Einstein 4-Manifolds
We prove a Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds with
asymptotic geometry at infinity. The asymptotic geometry at infinity is either
a cusp bundle over a compact space (the fibered cusps) or a fiber bundle over a
cone with a compact fiber (the fibered boundary). Many noncompact Einstein
manifolds come with such a geometry at infinity.Comment: 17 page
On the universal cover and the fundamental group of an -space
The main goal of the paper is to prove the existence of the universal cover
for -spaces. This generalizes earlier work of C. Sormani and the
second named author on the existence of universal covers for Ricci limit
spaces. As a result, we also obtain several structure results on the (revised)
fundamental group of such spaces. These are the first topological results for
-spaces without extra structural-topological assumptions (such as
semi-local simple connectedness).Comment: Final version to appear in Journal f\"ur die Reine und Angewandte
Mathemati
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