The scalar curvature problem on four-dimensional manifolds
Communications on Pure and Applied Analysis, 2020 We study the problem of existence of conformal metrics with prescribed scalar curvatures on a closed Riemannian \begin{document}$ 4 $\end{document} -manifold not conformally diffeomorphic to the standard sphere \begin{document}$ S^{4} $\end{document ...
H. Chtioui, H. Hajaiej, Marwa Soula
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Yamabe flow with prescribed scalar curvature [PDF]
Pacific Journal of Mathematics, 2017 In this work, we study the Yamabe flow corresponding to the prescribed scalar curvature problem on compact Riemannian manifolds with negative scalar curvature. The long time existence and convergence of the flow are proved under appropriate conditions on
Inas Amacha, R. Regbaoui
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Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature
, 2003 In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the $n$-sphere, with $n\geq 5$. Using tools from the theory of critical points at infinity, we provide some topological conditions on the ...
Ayed, Mohamed Ben, Mehdi, Khalil El
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Prescribing the Scalar Curvature Problem on Three and Four Manifolds
Advanced Nonlinear Studies, 2003 Abstract This paper is devoted to the prescribed scalar curvature problem on 3 and 4- dimensional Riemannian manifolds. We give a new class of functionals which can be realized as scalar curvature. Our proof uses topological arguments and the tools of the theory of the critical points at infinity.
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Metrics with Prescribed Ricci Curvature on Homogeneous Spaces
, 2016 Let $G$ be a compact connected Lie group and $H$ a closed subgroup of $G$. Suppose the homogeneous space $G/H$ is effective and has dimension 3 or higher. Consider a $G$-invariant, symmetric, positive-semidefinite, nonzero (0,2)-tensor field $T$ on $G/H$.
Pulemotov, Artem
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The Cauchy problems for Einstein metrics and parallel spinors
, 2013 We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W ...
A. Hermann +36 more
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On the volume functional of compact manifolds with boundary with constant scalar curvature
, 2008 We study the volume functional on the space of constant scalar curvature metrics with a prescribed boundary metric. We derive a sufficient and necessary condition for a metric to be a critical point, and show that the only domains in space forms, on ...
A.E. Fischer +17 more
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The prescribed Gauduchon scalar curvature problem in almost Hermitian geometry [PDF]
, 2022 Yuxuan Li, Wubin Zhou, Xianchao Zhou
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A prescribed scalar and boundary mean curvature problem and the Yamabe classification on asymptotically Euclidean manifolds with inner boundary [PDF]
, 2022 Vladmir Sicca, Gantumur Tsogtgerel
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Prescribing Scalar Curvature on S3, S4 and Related Problems
Journal of Functional Analysis, 1993 AbstractWe show that for the prescribing scalar curvature problem on Sn (n = 3, 4), we can perturb (in an explicit way) any given positive continuous function in any neighborhood of any given point on Sn such that for the perturbed function there exist many solutions.
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