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Annals of Global Analysis and Geometry

, Volume 42, Issue 2, pp 279–285 | Cite as

Integral Ricci curvature bounds along geodesics for nonexpanding gradient Ricci solitons

  • Bennett ChowEmail author
  • Peng Lu
  • Bo Yang
Article
  • 220 Downloads

Abstract

Following Li and Yau (Acta Math 156:153–201 1986) and similar to Perelman (The entropy formula for the Ricci flow and its geometric applications), we define an energy functional \({\mathcal{J}}\) associated to a smooth function \({\phi}\) on a complete Riemannian manifold. As an application, we deduce integral Ricci curvature upper bounds along modified geodesics for complete steady and shrinking gradient Ricci solitons.

Keywords

Ricci soliton Ricci flow Ricci curvature 

Mathematics Subject Classification (2000)

53C44 58J35 53C22 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA
  2. 2.Department of MathematicsUniversity of OregonEugeneUSA

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