We study a natural counterpart of the Nirenberg problem, namely to prescribe the Q-curvature of a conformal metric on the standard S^4 as a given function f. Our approach uses a geometric flow within the conformal class, which either leads to a solution of our problem as, in particular, in the case when f ≡ const, or otherwise induces a blow-up of the metric near some point of S4. Under suitable assumptions on f, also in the latter case the asymptotic behavior of the flow gives rise to existence results via Morse theory.

Q-curvature flow on S^4

Malchiodi, Andrea;Struwe, Michael
2006

Abstract

We study a natural counterpart of the Nirenberg problem, namely to prescribe the Q-curvature of a conformal metric on the standard S^4 as a given function f. Our approach uses a geometric flow within the conformal class, which either leads to a solution of our problem as, in particular, in the case when f ≡ const, or otherwise induces a blow-up of the metric near some point of S4. Under suitable assumptions on f, also in the latter case the asymptotic behavior of the flow gives rise to existence results via Morse theory.
2006
Settore MAT/05 - Analisi Matematica
   Variational Methods and Nonlinear Differential Equations.
   M.U.R.S.T.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/56102
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