- 636 Downloads
The aim of this chapter is to prove some uniqueness results for positive solutions of Yamabe-type equations. Our first theorem in this direction depends only on the sign of the coefficient \( b(x) \) of the nonlinear term and, loosely speaking, on an \( L^2 \)-type estimate of the distance, at infinity, of the two solutions under consideration. It is worth observing that this very general result is sharp and that the \( L^2 \)-type condition cannot be substituted with a corresponding \( L^p \) condition with \( p > 2 \)
KeywordsScalar Curvature Nonnegative Solution Complete Riemannian Manifold Geodesic Ball Complete Manifold
Unable to display preview. Download preview PDF.