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The cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding
theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s
because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature)
of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate
consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical
meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant
is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as
it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which
in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases
to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes. 相似文献
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Abraão Mendes 《Journal of Geometric Analysis》2018,28(2):1245-1257
In this paper, we obtain an analogue of Toponogov theorem in dimension 3 for compact manifolds \(M^3\) with nonnegative Ricci curvature and strictly convex boundary \(\partial M\). Here we obtain a sharp upper bound for the length \(L(\partial \Sigma )\) of the boundary \(\partial \Sigma \) of a free boundary minimal surface \(\Sigma ^2\) in \(M^3\) in terms of the genus of \(\Sigma \) and the number of connected components of \(\partial \Sigma \), assuming \(\Sigma \) has index one. After, under a natural hypothesis on the geometry of M along \(\partial M\), we prove that if \(L(\partial \Sigma )\) saturates the respective upper bound, then \(M^3\) is isometric to the Euclidean 3-ball and \(\Sigma ^2\) is isometric to the Euclidean disk. In particular, we get a sharp upper bound for the area of \(\Sigma \), when \(M^3\) is a strictly convex body in \(\mathbb {R}^3\), which is saturated only on the Euclidean 3-balls (by the Euclidean disks). We also consider similar results for free boundary stable CMC surfaces. 相似文献
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Guizellini Filipe Corrêa Franzin Bruno Trevizan da Silva Matheus Antonio Abra Luciana Mazotti Hojo Ossamu Pastre Iêda Aparecida Ribeiro Clóvis Augusto Paiva-Santos Carlos de Oliveira Fertonani Fernando Luis 《Journal of Thermal Analysis and Calorimetry》2021,143(1):47-60
Journal of Thermal Analysis and Calorimetry - The aim of this work is to synthesize and characterize a new structured silver–clay dried, calcined or sintered at different temperatures... 相似文献
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Abraão J.S. Capistrano 《Annalen der Physik》2018,530(1)
In this paper we examine the evolution of cosmic density parameters in a four‐dimensional space‐time embedded in a five‐dimensional bulk space. We show that the extrinsic curvature is an independent spin‐2 field governed by the Gupta equations. Without evoking a dark energy fluid, the corresponding cosmological model is compared with the phenomenological XCDM model and shows a good concordance with recent cosmological datasets from Planck Collaboration and the latest Baryons Acoustic Oscillations/Cosmic Microwave Background (BAO/CMBR) + SNIa studying the evolution of density parameters. In addition, a discussion on the coincidence problem is also proposed. 相似文献
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Abraçado LG Esquivel DM Alves OC Wajnberg E 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2005,175(2):309-316
Ferromagnetic resonance temperature dependence is used to study the magnetic material in smashed head, thorax, and abdomen of Solenopsis substituta ants. These three body parts present the five lines previously observed in other social insects. The magnetic material content is slightly higher in heads with antennae than in abdomen with petiole. Isolated nanoparticle diameters were estimated as 12.5 +/- 0.1 and 11.0 +/- 0.2 nm in abdomen with petiole and head with antennae, respectively. The presence of linear chains of these particles or large ellipsoidal particles are suggested. A bulk-like magnetite particle was observed in the thorax. The Curie-Weiss, the structural-electronic and ordering transition temperatures were obtained in good agreement with those proposed for magnetite nanoparticles. 相似文献
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