On the singular prescribed scalar curvature problem
, 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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Non-degeneracy of multi-bubbling solutions for prescribed scalar curvature problem via local Pohozaev identity [PDF]
, 2022 Abstract This paper deals with the following nonlinear elliptic equation$$-\Delta u=Q(|y'|,y'')u^{\frac{N+2}{N-2}},\,\,u>0,\,\,\text{in}\R^N,\,\,u\inD^{1,2}(\R^{N}),$$where $(y',y'')\in \R^2\times\R^{N-2}$,$Q(|y'|,y'')$ is a bounded non-negative function in$\mathbb{R}^{2}\times \R^{N-2}$.
Qingfang Wang
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Prescribed Scalar Curvature Problem under Conformal Deformation of A Riemannian Metric with Dirichlet Boundary Condition [PDF]
, 2022 V1, Aug.
Jie Xu
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Prescribed scalar curvature problem on complete manifolds
Journal de Mathématiques Pures et Appliquées, 2001 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.
David Holcman
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Infinitely many solutions for the prescribed scalar curvature problem with volcano-like curvature [PDF]
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T. Li, Juncheng Wei, H. Yang
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On the prescribed scalar curvature problem in
Journal de Mathématiques Pures et Appliquées, 2015 Yinbin Deng +2 more
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Conformally Prescribed Scalar Curvature on Orbifolds [PDF]
Communications in Mathematical Physics, 2021 We study the prescribed scalar curvature problem in a conformal class on orbifolds with isolated singularities. We prove a compactness theorem in dimension 4, and an existence theorem which holds in dimensions $$n \ge 4$$ n ≥ 4 .
Tao Ju, Jeff Viaclovsky
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Singular Riemannian Foliations and the prescribing scalar curvature problem
, 2021 An orbit-like foliation is a singular foliation on a complete Riemannian manifold $M$ whose leaves are locally equidistant (i.e., a singular Riemannian foliation) and (transversely) infinitesimally homogenous. This class of singular foliation contains not only the classe of partion of the space into orbits of isometric actions, but also infinite many ...
Alexandrino, Marcos M. +1 more
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Infinitely many solutions to the Yamabe problem on noncompact manifolds [PDF]
, 2018 We establish the existence of infinitely many complete metrics with constant scalar curvature on prescribed conformal classes on certain noncompact product manifolds.
Bettiol, R., Piccione, P.
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The constraint equations for the Einstein-scalar field system on compact manifolds [PDF]
, 2006 We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations.
Andersson L +26 more
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