Results 1 to 10 of about 29,420 (189)
The prescribed Gauduchon scalar curvature problem in almost Hermitian geometry [PDF]
Science China Mathematics, 2023 In this paper we consider the prescribed Gauduchon scalar curvature problem on almost Hermitian manifolds. By deducing the expression of the Gauduchon scalar curvature under the conformal variation, the problem is reduced to solve a semi-linear partial differential equation with exponential nonlinearity.
Li, Yuxuan, Zhou, Wubin, Zhou, Xianchao
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Topological tools for the prescribed scalar curvature problem on S n
Open Mathematics, 2014 AbstractIn this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, 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 well known results due to Y. Li [16].
Abuzaid Dina +3 more
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The Prescribed Chern Scalar Curvature Problem [PDF]
The Journal of Geometric Analysis, 2022 AbstractThe paper is an attempt to resolve the prescribed Chern scalar curvature problem. We look for solutions within the conformal class of a fixed Hermitian metric. We divide the problem in three cases, according to the sign of the Gauduchon degree, that we analyse separately.
Elia Fusi
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Doubling the equatorial for the prescribed scalar curvatureproblem on ${\mathbb{S}}^N$ [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2023 Abstract Note: Please see pdf for full abstract with equations. We consider the prescribed scalar curvature problem on SN ΔSN v −N(N − 2)/2 v + K̃ (y)v N+2/N−2 = 0 on SN, v > 0 in SN, under the assumptions that the scalar curvature K̃ is rotationally symmetric, and has a positive local maximum point between the poles.
Duan, Lipeng, Musso, Monica, Wei, Suting
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On the singular prescribed scalar curvature problem [PDF]
, 2023 Let (M, g) be a compact Riemannian manifold of dimension \(n \geq3\). In this paper, we define and introduce the prescribed scalar curvature problem with singularities. Under some assumptions, we show that there exists a conformal metric \(\overline{g}\) such that its scalar curvature \(S_{\overline{g}}\) equals some given function.
Hichem Boughazi
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The prescribed scalar curvature problem for metrics with unit total volume [PDF]
Mathematische Annalen, 2014 We solve the modified Kazdan-Warner problem of finding metrics with prescribed scalar curvature and unit total volume.
Shinichiroh Matsuo
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On the Chen–Lin Conjecture for the Prescribed Scalar Curvature Problem
The Journal of Geometric Analysis, 2023 We prove a criterion of existence of solutions conjectured by C. C. Chen and C. S. Lin [20] for the prescribed scalar curvature problem on the standard n-dimensional sphere.
H. Chtioui
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The Journal of Geometric Analysis, 2023 25 ...
Vladmir Sicca, Gantumur Tsogtgerel
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Prescribed scalar curvature problem on complete manifolds
Journal de Mathématiques Pures et Appliquées, 1999 Summary: Conditions on the geometric structure of a complete Riemannian manifold are given to solve the prescribed scalar curvature problem. In some cases, the conformal metric obtained is complete. A minimizing sequence is constructed which converges strongly to a solution.
D. Holcman
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On the prescribed scalar curvature problem on 4-manifolds
Duke Mathematical Journal, 1996 This work gives a complete and detailed proof of the result stated in the appendix of the paper of \textit{A. Bahri} and \textit{J. M. Coron} [J. Funct. Anal. 95, No. 1, 106-172 (1991; Zbl 0722.53032)]. The key part in the proof is to find a good pseudo-gradient flow. This is hard work. To do this, they need to find a good Morse lemma at bubbles. It is
Ben Ayed, Mohamed +3 more
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