منابع مشابه
PRESCRIBING SCALAR CURVATURE ON Sn
on S for n ≥ 3. In the case R is rotationally symmetric, the well-known Kazdan-Warner condition implies that a necessary condition for (1) to have a solution is: R > 0 somewhere and R′(r) changes signs. Then, (a) is this a sufficient condition? (b) If not, what are the necessary and sufficient conditions? These have been open problems for decades. In Chen & Li, 1995, we gave question (a) a nega...
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In this paper, we describe great details of the bubbling behavior for a sequence of solutions wi of Lwi +Riw n+2 n−2 i = 0 on S , where L is the conformal Laplacian operator of (Sn, g0) and Ri = n(n−2)+ tiR̂, R̂ ∈ C1(Sn). As ti ↓ 0, we prove among other things the location of blowup points, the spherical Harnack inequality near each blowup point and the asymptotic formulas for the interaction of ...
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This is a sequel to [30], which studies the prescribing scalar curvature problem on S". First we present some existence and compactness results for n = 4. The existence result extends that of Bahri and Coron [4], Benayed, Chen, Chtioui, and Hammami [6], and Zhang [39]. The compactness results are new and optimal. In addition, we give a counting formula of all solutions. This counting formula, t...
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In this paper we formulate new curvature functions on Sn via integral operators. For certain even orders, these curvature functions are equivalent to the classic curvature functions defined via differential operators, but not for all even orders. Existence result for antipodally symmetric prescribed curvature functions on Sn is obtained. As a corollary, the existence of a conformal metric for a...
متن کاملPrescribing Ricci Curvature on Complexified Symmetric Spaces
The complexification of the compact group G is the group G whose Lie algebra is the complexification of the Lie algebra g of G and which satisfies π1(G ) = π1(G). The complexification G/K of G/K can be then identified (G-equivariantly) with the tangent bundle of G/K. We also remark that the Kähler form obtained in the Theorem is exact. This result has been proved in [9] for symmetric spaces of ...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2007
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2006.03.004