Advertisement

A priori estimates

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

Abstract

In this chapter we determine a priori estimates on the behavior at infinity of positive solutions of the equation
$$ \Delta u + a(x)u-b(x)u^{\sigma} \geq 0, \,\,\,\, \sigma > 1 $$
(4.1)
on M under assumptions on \( a(x) \) and \( b(x) \) related to the geometrical requirement
$$ \mathrm{Ric} \geq-(m-1)H^{2}(1+r(x)^{2})^{\frac{\delta}{2}} $$
(4.2)
for some\( H > 0 \) and \( \delta\,\, \epsilon\,\, \mathbb{R} \).

Keywords

Ricci Curvature Ricci Tensor Complete Riemannian Manifold Nonexistence Result 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations