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Uniqueness

  • Paolo Mastrolia
  • Marco Rigoli
  • Alberto G. Setti
Chapter
  • 636 Downloads
Part of the Progress in Mathematics book series (PM, volume 302)

Abstract

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 \( p > 2 \)

Keywords

Scalar Curvature Nonnegative Solution Complete Riemannian Manifold Geodesic Ball Complete Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  • Paolo Mastrolia
    • 1
  • Marco Rigoli
    • 1
  • Alberto G. Setti
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi die MilanoMilanoItaly
  2. 2.Dipartimento di Fisica e MatematicaUniversità dell’InsubriaComoItaly

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