Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606271 | Differential Geometry and its Applications | 2011 | 20 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Stefano Pigola, Giona Veronelli,