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RESEARCH BLOG 7/23/03 Let (M, g) be a Riemannian manifold. Recall that we defined
 

Summary: RESEARCH BLOG 7/23/03
Let (M, g) be a Riemannian manifold. Recall that we defined
(g, ) = inf{
M
[(| u|2
+ R) + u]e-u
dV - n -
n
2
ln(4)
|
M
e-u
dV = 1}.
(see research blog 7/21/03 ). We will use V k
n (r) to denote the volume
of a ball of radius r in the simply-connected space form of sectional
curvature k of dimension n, and Br(x) = Br(x, g) denotes the ball of
radius r in M centered at the point x in the metric g.
Lemma 0.1. Suppose that R(g) ^R, and Ric(g) (n - 1)kg, then

  

Source: Agol, Ian - Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

 

Collections: Mathematics