Results 21 to 30 of about 524 (55)
Prescribing eigenvalues of the Dirac operator
, 2005 In this note we show that every compact spin manifold of dimension $\geq 3$ can be given a Riemannian metric for which a finite part of the spectrum of the Dirac operator consists of arbitrarily prescribed eigenvalues with multiplicity 1.Comment: To ...
Bär +7 more
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On subsolutions and concavity for fully nonlinear elliptic equations
Advanced Nonlinear StudiesSubsolutions and concavity play critical roles in classical solvability, especially a priori estimates, of fully nonlinear elliptic equations. Our first primary goal in this paper is to explore the possibility to weaken the concavity condition.
Guan Bo
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Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators
, 2006 We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the derivative of a ...
Campos R. G. +8 more
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Deformations of 2k-Einstein structures
, 2010 It is shown that the space of infinitesimal deformations of 2k-Einstein structures is finite dimensional at compact non-flat space forms. Moreover, spherical space forms are shown to be rigid in the sense that they are isolated in the corresponding ...
Berger +10 more
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Advances in Nonlinear AnalysisLet (ℳ,g)\left({\mathcal{ {\mathcal M} }},g) and (K,κ)\left({\mathcal{K}},\kappa ) be two Riemannian manifolds of dimensions NN and mm, respectively. Let ω∈C2(ℳ)\omega \in {C}^{2}\left({\mathcal{ {\mathcal M} }}) satisfy ω>0\omega \gt 0.
Chen Wenjing, Wang Zexi
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Comparison formulas for total mean curvatures of Riemannian hypersurfaces
Advanced Nonlinear StudiesWe devise some differential forms after Chern to compute a family of formulas for comparing total mean curvatures of nested hypersurfaces in Riemannian manifolds.
Ghomi Mohammad
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Advanced Nonlinear StudiesIn this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia +2 more
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Overtwisted energy-minimizing curl eigenfields
, 2015 We consider energy-minimizing divergence-free eigenfields of the curl operator in dimension three from the perspective of contact topology. We give a negative answer to a question of Etnyre and the first author by constructing curl eigenfields which ...
Arnold V +14 more
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Examples of non-isolated blow-up for perturbations of the scalar curvature equation on non locally conformally flat manifolds [PDF]
, 2014 Solutions to scalar curvature equations have the property that all possible blow-up points are isolated, at least in low dimensions. This property is commonly used as the first step in the proofs of compactness. We show that this result becomes false for
Robert, Frédéric, Vétois, Jérôme
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On the Riemannian Penrose inequality with charge and the cosmic censorship conjecture [PDF]
, 2012 We note an area-charge inequality orignially due to Gibbons: if the outermost horizon $S$ in an asymptotically flat electrovacuum initial data set is connected then $|q|\leq r$, where $q$ is the total charge and $r=\sqrt{A/4\pi}$ is the area radius of $S$
Khuri, Marcus A +2 more
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