Lower bounds for warping functions on warped-product AHE manifolds

Details Lower bounds for warping functions on warped-product AHE manifolds Lower bounds for warping functions on warped-product AHE manifolds

2007-10-14

arxiv.org/abs/0710.2699v1

Mathematics

Differential Geometry

7 pages

Scientific paper

Let $[\gamma]$ be the conformal boundary of a warped product $C^{3,\alpha}$
AHE metric $g=g_M+u^2h$ on $N=M \times F$, where $(F,h)$ is compact with unit
volume and nonpositive curvature. We show that if $[\gamma]$ has positive
Yamabe constant, then $u$ has a positive lower bound that depends only on
$[\gamma]$.

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