Lower bounds for warping functions on warped-product AHE manifolds

Abstract

Let $[\gamma ]$ be the conformal boundary of a warped product $C^{3,\alpha }$ AHE metric $g=g_M+u^{2}h$ 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 $[\gamma ]$.

7 pages