Scalar curvature and warped products of Riemann manifolds
F. Dobarro,E. Lami Dozo +1 more
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In this article, the relationship between the scalar curvature of a warped product M Xf N of Riemann manifolds and those ones of M and N was established and the weights f were found to obtain constant curvatures on M X f N when M is compact.Abstract:
We establish the relationship between the scalar curvature of a warped product M Xf N of Riemann manifolds and those ones of M and N. Then we search for weights f to obtain constant scalar curvature on M Xf N when M is compact.read more
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Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops
TL;DR: In this article, Drukker, Giombi, Ricci and Trancanelli show that expectation values of certain 1/8 BPS supersymmetric Wilson loops on S petertodd 2 in the 4d $ \mathcal{N}=4 $¯¯¯¯ SYMiscapturedbythe2dcHYMtheory.
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Curvature of multiply warped products
Fernando Dobarro,Bülent Ünal +1 more
TL;DR: In this paper, the authors studied Ricci-flat and Einstein-Lorentzian multiply warped products and applied their results to other relativistic space-times, i.e., Reissner-Nordstrom, Kasner space times, Banados-Teitelboim-Zanelli and de Sitter black hole solutions.
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Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops
TL;DR: In this article, Drukker, Giombi, Ricci and Trancanelli showed that expectation values of certain 1/8 BPS supersymmetric Wilson loops on S^2 in the 4d N=4 super Yang-Mills theory are captured by the 2d cHYM theory.
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Constant scalar curvatures on warped product manifolds
TL;DR: In this paper, the problem of showing when a Riemannian metric of constant scalar curvature can be produced on a product manifold by a warped product construction applied to the two RiemANNIAN manifolds (B,gB) and (F,gF) was studied.
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On Semilinear Elliptic Equations Involving Concave and Convex Nonlinearities
TL;DR: In this paper, the authors prove existence results for the problem with 0 < q < 1 < p depending on the range of parameters λ and μ and use the variational method based on a constrained minimization combined with concentration-compactness principle at infinity.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
TL;DR: A survey of nonlinear functional analysis in ordered Banach spaces can be found in this paper, where some of the most important methods and results of non-linear functional analyses are discussed.
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Some global results for nonlinear eigenvalue problems
TL;DR: In this paper, the structure of the solution set for a large class of nonlinear eigenvalue problems in a Banach space is investigated, and the existence of continua, i.e., closed connected sets, of solutions of these equations is demonstrated.
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