Compactness for conformal metrics with constant Q curvature on locally conformally flat manifolds
نویسندگان
چکیده
منابع مشابه
Compactness for Conformal Metrics with Constant Q Curvature on Locally Conformally Flat Manifolds
In this note we study the conformal metrics of constant Q curvature on closed locally conformally flat manifolds. We prove that for a closed locally conformally flat manifold of dimension n ≥ 5 and with Poincarë exponent less than n−4 2 , the set of conformal metrics of positive constant Q and positive scalar curvature is compact in the C∞ topology.
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Abstract. We study the equation ∆gu− n−2 4(n−1)R(g)u+Ku p = 0 (1+ ζ ≤ p ≤ n+2 n−2 ) on locally conformally flat compact manifolds (M, g). We prove the following: (i) When the scalar curvature R(g) > 0 and the dimension n ≥ 4, under suitable conditions on K, all positive solutions u have uniform upper and lower bounds; (ii) When the scalar curvature R(g) ≡ 0 and n ≥ 5, under suitable conditions ...
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2006
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-006-0010-8