Results 11 to 20 of about 7,385 (153)
On the bifurcation of solutions of the Yamabe problem in product manifolds with minimal boundary
Advances in Nonlinear Analysis, 2018 In this paper, we study the multiplicity of solutions of the Yamabe problem on product manifolds with minimal boundary via bifurcation theory.
Cárdenas Diaz Elkin Dario +1 more
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On a fully nonlinear Yamabe problem [PDF]
Annales Scientifiques de l’École Normale Supérieure, 2006 We solve the $ _2$-Yamabe problem for a non locally conformally flat manifold of dimension $n>8$.
Ge, Yuxin, Wang, Guofang
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Equivariant Yamabe problem and Hebey–Vaugon conjecture
Journal of Functional Analysis, 2010 In their study of the Yamabe problem in the presence of isometry group, Hebey and Vaugon announced a conjecture. This conjecture generalizes Aubin's conjecture, which has already been proven and is sufficient to solve the Yamabe problem. In this paper, we generalize Aubin's theorem and we prove the Hebey--Vaugon conjecture in some new cases.
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Bulletin of the American Mathematical Society, 1987 This is a basically self-contained account of the solution to the Yamabe problem, covering the steps due to Yamabe, Trudinger, Aubin and Schoen and including Witten's proof of the positive mass theorem. The presentation contains various improvements over arguments existing in the literature.
Lee, John M., Parker, Thomas H.
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The Neumann problem on the domain in 𝕊3 bounded by the Clifford torus
Advanced Nonlinear Studies, 2023 In this study, the solution of the Neumann problem associated with the CR Yamabe operator on a subset Ω\Omega of the CR manifold S3{{\mathbb{S}}}^{3} bounded by the Clifford torus Σ\Sigma is discussed.
Case Jeffrey S. +4 more
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Results in Applied Mathematics, 2021 We consider a nonlinear partial differential equation of Yamabe-type. In Boucheche (2019), it has been proved that the problem admits a solution under the assumption that the gradient of the associated variational functional is lower bounded by a ...
Khadijah Sharaf
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A note on Chern-Yamabe problem [PDF]
Differential Geometry and its Applications, 2020 We propose a flow to study the Chern-Yamabe problem and discuss the long time existence of the flow. In the balanced case we show that the Chern-Yamabe problem is the Euler-Lagrange equation of some functional. The monotonicity of the functional along the flow is derived. We also show that the functional is not bounded from below.
Calamai, Simone, Zou, Fangyu
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Equivariant Yamabe problem with boundary [PDF]
Calculus of Variations and Partial Differential Equations, 2022 AbstractAs a generalization of the Yamabe problem, Hebey and Vaugon considered the equivariant Yamabe problem: for a subgroupGof the isometry group, find aG-invariant metric whose scalar curvature is constant in a given conformal class. In this paper, we study the equivariant Yamabe problem with boundary.
Ho, Pak Tung, Shin, Jinwoo
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Surveys in Differential Geometry, 2012 1.1. The k-Yamabe problem. The k-Yamabe problem is a higher order extension of the celebrated Yamabe problem for scalar curvature. It was initially proposed by Viaclovsky [72] and also arose in the study of Q-curvatures in [11]. Viaclovsky found that in a conformal metric, the resultant k-curvature equation can be expressed as an equation similar to ...
Sheng, Weimin +2 more
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$$\sigma _{2}$$ Yamabe problem on conic 4-spheres [PDF]
Calculus of Variations and Partial Differential Equations, 2019 Comment: 20 pages, we makes some changes in the paper posted ...
Fang, Hao, Wei, Wei
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