Siberian Mathematical Journal

, Volume 58, Issue 6, pp 1004–1011 | Cite as

Evolution of the Yamabe Constant Under Bernhard List’s Flow

Article
  • 2 Downloads

Abstract

Let g(t) be a solution of Bernhard List’s flow on a closed manifold. We obtain a pointwise control on the volume of g(t). Then under an essential assumption, we achieve a formula for the evolution of the Yamabe constant Y(g(t)) when g(t) is evolving by Bernhard List’s flow.

Keywords

Bernhard List’s flow Yamabe constant maximum principle 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    List B., Evolution of an Extended Ricci Flow System, Ph. D. Thesis, AEI Potsdam (2006).MATHGoogle Scholar
  2. 2.
    DeTurck D., “Deforming metrics in the direction of their Ricci tensors,” J. Differ. Geom., vol. 18, no. 1, 157–162 (1983).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    List B., “Evolution of an extended Ricci flow system,” Comm. Anal. Geom., vol. 16, no. 5, 1007–1048 (2008).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Chow B. and Knopf D., The Ricci Flow: An Introduction, Amer. Math. Soc., Providence (2004).CrossRefMATHGoogle Scholar
  5. 5.
    Chang S.-C. and Lu P., “Evolution of Yamabe constant under Ricci flow,” Ann. Global Anal. Geom., vol. 31, no. 2, 147–153 (2007).MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Aubin T., “Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire,” J. Math. Pures Appl., vol. 55, no. 9, 269–296 (1976).MathSciNetMATHGoogle Scholar
  7. 7.
    Aubin T., Some Nonlinear Problems in Riemannian Geometry, Springer-Verlag, Berlin (1998).CrossRefMATHGoogle Scholar
  8. 8.
    Lee J. and Parker T., “The Yamabe problem,” Bull. Amer. Math. Soc., vol. 17, no. 1, 37–91 (1987).MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Schoen R., “Conformal deformation of a Riemannian metric to constant scalar curvature,” J. Differ. Geom., vol. 20, no. 2, 478–495 (1984).MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Trudinger N., “Remarks concerning the conformal deformation of metrics to constant scalar curvature,” Ann. Sc. Norm. Super. Pisa, vol. 22, no. 2, 265–274 (1968).MathSciNetMATHGoogle Scholar
  11. 11.
    Koiso N., “A decomposition of the space M of Riemannian metrics on a manifold,” Osaka J. Math., vol. 16, no. 2, 423–429 (1979).MathSciNetMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceShahid Bahonar University of KermanKermanIran

Personalised recommendations