Symmetry, Integrability and Geometry: Methods and Applications, 2007 The $(2k)$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k)$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k = 1$.
Mohammed Larbi Labbi
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Volume comparison and the sigma_k-Yamabe problem
, 2002 In this paper we study the problem of finding a conformal metric with the property that the k-th elementary symmetric polynomial of the eigenvalues of its Weyl-Schouten tensor is constant. A new conformal invariant involving maximal volumes is defined, and this invariant is then used in several cases to prove existence of a solution, and compactness of
Gursky, Matthew J., Viaclovsky, Jeff A.
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Successful treatment of ejaculation pain with silodosin in patient with Zinner syndrome: a case report. [PDF]
Transl Androl Urol, 2023 Uetani M +9 more
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Energy Quantization for Yamabe's problem in Conformal Dimension
Electronic Journal of Differential Equations, 2006 T. Riviere proved an energy quantization for Yang-Mills fields defined on n-dimensional Riemannian manifolds, when $n$ is larger than the critical dimension 4. More precisely, he proved that the defect measure of a weakly converging sequence of Yang-Mills fields is quantized, provided the $W^{2,1}$ norm of their curvature is uniformly bounded.
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The Yamabe problem with singularities
, 2008 Let $(M,g)$ be a compact Riemannian manifold of dimension $n\geq 3$. Under some assumptions, we prove that there exists a positive function $ $ solution of the following Yamabe type equation + h = \tilde h ^{\frac{n+2}{n-2}} where $h\in L^p(M)$, $p>n/2$ and $\tilde h\in \mathbb R$. We give the regularity of $ $ with respect to the value of $
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The Yamabe problem on CR manifolds
Journal of Differential Geometry, 1987 The Yamabe problem is to find a metric of constant scalar curvature in a given conformal class of Riemannian metrics. This paper studies the analogous problem for strictly pseudoconvex CR-manifolds. The notion of scalar curvature used here is due to S. Webster. After introducing the relevant variational problem for CR manifolds an invariant \(\lambda\)
Jerison, David, Lee, John M.
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The Influence of Dysphagia on Nutritional and Frailty Status among Community-Dwelling Older Adults. [PDF]
Nutrients, 2021 Nishida T, Yamabe K, Honda S.
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Comparison of Hybrid Posterior Fixation and Conventional Open Posterior Fixation Combined with Multilevel Lateral Lumbar Interbody Fusion for Adult Spinal Deformity. [PDF]
J Clin Med, 2022 Endo H +6 more
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Verification of Coronary Computed Tomography-Derived Fractional Flow Reserve Measurement Site for Detection of Significant Coronary Artery Disease. [PDF]
Circ Rep, 2021 Kawasaki T +12 more
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Recent progress on the Yamabe problem
, 2010 We give a survey of various compactness and non-compactness results for the Yamabe equation. We also discuss a conjecture of Hamilton concerning the asymptotic behavior of the parabolic Yamabe flow.
Brendle, S., Marques, F. C.
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