Prescribed Q-curvature on manifolds of even dimension

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Abstract

Given a compact even dimensional manifold and a prescribed function f, under suitable hypotheses, we prove the existence of conformal metrics with Q-curvature f. We use a variational method which allows the corresponding Graham–Jenne–Mason–Sparling operator to have negative eigenvalues.

MSC

35J35
53A30
53C21

Keywords

Geometric PDEs
Variational method
Min–max scheme
Q-curvature

Cited by (0)

1

Supported by the Agence Nationale de Recherche project Flots et opérateurs géométriques ANR-07-BLAN-0251-01.