Geodesic
Partial Differential Equations/Differential Geometry
Q-curvature flow with indefinite nonlinearity
[Flot de Q-courbure pour une non-linéarité indéfinie]

Présenté par : Paul Malliavin

Ma, Li1 ; Liu, B.1
1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Comptes Rendus. Mathématique, Tome 348 (2010) no. 7-8, pp. 403-406.

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In this Note, we study Q-curvature flow on S4 with indefinite nonlinearity. Our result is that the prescribed Q-curvature problem on S4 has a solution provided the prescribed non-negative Q-curvature f has its positive part, which possesses non-degenerate critical points such that ΔS4f≠0 at the saddle points and an extra condition such as a nontrivial degree counting condition.

Dans cette Note on étudie le flot de Q-courbure sur S4 dans le cas d'une non-linéarité indéfinie. Le résultat montre que le problème de la Q-courbure imposée sur S4 a une solution à condition que la Q-courbure non négative imposée f ait une partie strictement positive et des points critiques non dégénérés tels que ΔS4f≠0 aux points selles et une condition supplémentaire du type condition non triviale sur le degré.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.02.014

Ma, Li 1 ; Liu, B. 1

1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China 
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Ma, Li; Liu, B. Q-curvature flow with indefinite nonlinearity. Comptes Rendus. Mathématique, Tome 348 (2010) no. 7-8, pp. 403-406. doi : 10.1016/j.crma.2010.02.014. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2010.02.014/

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☆ The research is partially supported by the National Natural Science Foundation of China 10631020 and SRFDP 20090002110019.