O ct 2 00 2 A conformal invariant related to some fully nonlinear equations

  title={O ct 2 00 2 A conformal invariant related to some fully nonlinear equations},
  author={Matthew J. Gursky and Jeff A. Viaclovsky},
In this paper we study the problem of finding a conformal metric with the property that the k-th elementary symmetric polynomial of the eigenvalues of its Weyl-Schouten tensor is constant. A new conformal invariant involving maximal volumes is defined, and this invariant is then used in several cases to prove existence of a solution, and compactness of the space of solutions (provided the conformal class admits an admissible metric). In particular, the problem is completely solved in dimension… CONTINUE READING

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