Prescribing symmetric functions of the eigenvalues of the Ricci tensor

Details Prescribing symmetric functions of the eigenvalues of the Ricci tensor Prescribing symmetric functions of the eigenvalues of the Ricci tensor

2004-09-10

arxiv.org/abs/math/0409187v2

Final version: Annals of Mathematics 166 (2007) no. 2, 475-531

Mathematics

Differential Geometry

53 pages; revised version to appear in Annals of Mathematics

Scientific paper

We study the problem of conformally deforming a metric to a prescribed
symmetric function of the eigenvalues of the Ricci tensor. We prove an
existence theorem for a wide class of symmetric functions on manifolds with
positive Ricci curvature, provided the conformal class admits an admissible
metric.

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