Results 11 to 20 of about 29,420 (189)
On the prescribed scalar curvature problem on the three-dimensional half sphere [PDF]
Pacific Journal of Mathematics, 2005 We provide a variety of classes of functions that can be realized as the scalar curvature of the standard three-dimensional half sphere with respect to some metric whose boundary mean curvature is zero. Such a problem is nontrivial, since we have to overcome topological obstructions.
Mohamed Ben Ayed, Hichem Chtioui
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Existence and Multiplicity Results for the Prescribed Webster Scalar Curvature Problem on Three CR Manifolds [PDF]
Journal of Geometric Analysis, 2011 This paper is devoted to the existence of contact forms of prescribed Webster scalar curvature on a $3-$dimensional CR compact manifold locally conformally CR equivalent to the unit sphere $\mathbb{S}^{3}$ of $\mathbb{C}^{2}$. Due to Kazdan-Warner type obstructions, conditions on the function $H$ to be realized as a Webster scalar curvature have to be ...
Hichem Chtioui +2 more
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Constructing solutions for the prescribed scalar curvature problem via local Pohozaev identities
Journal of Differential Equations, 2019 Abstract This paper deals with the following prescribed scalar curvature problem − Δ u = Q ( | y ′ | , y ″ ) u N + 2 N − 2 , u > 0 , y = ( y ′ , y ″ ) ∈ R 2 × R N − 2 , where Q ( y ) is nonnegative and bounded.
Shuangjie Peng, Chunhua Wang, Suting Wei
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On the prescribed scalar curvature problem on S: Part 1, asymptotic estimates and existence results
Differential Geometry and its Applications, 2016 Abstract There have been many works on the problem of finding a conformal metric on the standard sphere S n , n ≥ 3 , when the prescribed scalar curvature function is flat near its critical points with order of flatness β . All the existence results up to this research concern the case 1 β n .
Khadijah Sharaf
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The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space
Calculus of Variations and Partial Differential Equations, 2003 In this nice paper the author extend recent work by \textit{P. Bayard} [Calc. Var. Partial Differ. Equ. 18, No. 1, 1--30 (2003; Zbl 1043.53027)] on the Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space. Among other results, the authors prove a maximum principle for the curvature of spacelike admissible solutions of ...
J. Urbas
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Topological methods for the prescribed Webster Scalar Curvature problem on CR manifolds
Differential Geometry and its Applications, 2010 AbstractWe consider the existence of contact forms of prescribed Webster scalar curvature on a (2n+1)-dimensional CR compact manifold locally conformally CR equivalent to the standard unit sphere S2n+1 of Cn+1. We give some existence results, using dynamical and topological methods involving the study of the critical points at infinity of the ...
Mohameden Ould Ahmedou +2 more
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Infinitely many solutions for the prescribed scalar curvature problem on
Journal of Functional Analysis, 2010 AbstractWe consider the following prescribed scalar curvature problem on SN(∗){−ΔSNu+N(N−2)2u=K˜uN+2N−2onSN,u>0 where K˜ is positive and rotationally symmetric. We show that if K˜ has a local maximum point between the poles then Eq. (∗) has infinitely many non-radial positive solutions, whose energy can be made arbitrarily large.
Juncheng Wei, Shusen Yan
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On the prescribed scalar curvature problem in
Journal de Mathématiques Pures et Appliquées, 2015 Abstract We obtain a local uniqueness result for bubbling solutions of the prescribed scalar curvature problem in R N . Such a result implies that some bubbling solutions preserve the symmetry from the scalar curvature K ( y ) .
Shusen Yan, Yinbin Deng, Chang-Shou Lin
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Correction: On the Chen–Lin Conjecture for the Prescribed Scalar Curvature Problem
The Journal of Geometric Analysis, 2023 H. Chtioui
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On the prescribed scalar curvature problem on
Comptes Rendus. Mathématique, 2012 In this Note, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere Sn, n⩾3. We give new existence and multiplicity results based on a new Euler–Hopf formula type. Our argument also has the advantage of extending the well known results due to Y. Li (1995) [10].
Randa Ben Mahmoud +2 more
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