Article ID Journal Published Year Pages File Type
4606271 Differential Geometry and its Applications 2011 20 Pages PDF
Abstract

We prove uniform decay estimates at infinity for solutions 0⩽u∈Lp0⩽u∈Lp of the semilinear elliptic inequality Δu+auσ+bu⩾0Δu+auσ+bu⩾0, a,b⩾0a,b⩾0, σ⩾1σ⩾1, in the presence of a Sobolev inequality (with potential term). This gives a unified point of view in the investigation of different geometric questions. In particular, we present applications to the study of the topology at infinity of parallel mean curvature submanifolds, to the non-compact Yamabe problem, and to estimate the decay rate of the traceless Ricci tensor of conformally flat manifolds.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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