Conformal metrics on with constant -curvature and large volume

  • Luca Martinazzi

    Rutgers University, United States

Abstract

We study conformal metrics on with constant -curvature (notice that is the -curvature of ) and finite volume. When we show that there exists such that for any there is a conformal metric on with and . This is in sharp contrast with the four-dimensional case, treated by C.-S. Lin. We also prove that when is odd and greater than , there is a constant such that for every there is a conformal metric on with , . This extends a result of A. Chang and W.-X. Chen. When is even we prove a similar result for conformal metrics of negative -curvature.

Cite this article

Luca Martinazzi, Conformal metrics on with constant -curvature and large volume. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 6, pp. 969–982

DOI 10.1016/J.ANIHPC.2012.12.007