Let B be the unit ball in RN with N≥2. Let f∈C1(0,∞),R), f(0)=0, f(β)=β for some β∈(0,∞), f(s)<sfors∈(0,β),f(s)>sfors∈(β,∞) and f′(β)>λkr, where λkr is the k-th radial eigenvalue of −Δ+I in the unit ...ball with Neumann boundary condition. We use the unilateral global bifurcation theorem to show the existence of nonconstant, positive radial solutions of the quasilinear Neumann problem−div(∇u1−|∇u|2)+u=f(u)inB,∂νu=0on∂B.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Based on the first law of black hole thermodynamics, we yield the metric of geometrothermodynamics. Choosing a hypersurface of constant extensive variable, the extrinsic curvature scalar is ...calculated and general correspondence of singularities between the extrinsic curvature scalar and the specific heat is discovered. This correspondence is further shown to exist in the constant intensive variable ensemble. We also show that extrinsic curvature scalar can reflect thermodynamic stability information, in spite of considering fluctuations of different thermodynamic variables or choosing different hypersurfaces.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
We take advantage of the Shiromizu et al. covariant formalism to find out the brane properties originating from the five dimensional bulk spacetime. Making a different choice for the conformal factor ...e−2b(z) compared to Estrada (0000), we reach a new solution with a lot of interesting properties, where b(z)=ln(1/cosh2μz). The non-local tensor Eab rooted from the 5-dimensional Riemann tensor gives an anisotropic stress energy tensor on the brane with positive energy density and negative radial pressure. The BH on the brane looks like a black string in the 5-dimensional space, with no singularities of the curvature invariants.
•The curvature invariants are finite for any values of the coordinates.•The energy density of the induced stress tensor is positive and finite.•The stress tensor related to the tidal effects depend on the fifth coordinate.•The radial acceleration changes its sign when the radial coordinate r=k.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Abstract
The results on the initial boundary value problem for Einstein’s vacuum field equation obtained in Friedrich and Nagy
Commun. Math. Phys.
201
619–655 rely on an unusual gauge. One of the ...defining gauge source functions represents the mean extrinsic curvature of the time-like leaves of a foliation that includes the boundary and covers a neighbourhood of it. The others steer the development of a frame field and coordinates on the leaves. In general their combined action is needed to control in the context of the reduced field equations the evolution of the leaves. In this article are derived the hyperbolic equations implicit in that gauge. It is shown that the latter are independent of the Einstein equations and well defined on arbitrary space-times. The analysis simplifies if boundary conditions with constant mean extrinsic curvature are stipulated. It simplifies further if the boundary is required to be totally geodesic.
In this paper, using Arnowitt-Deser-Misner (ADM) decomposition formalism, we first obtain a neutral black hole solution for consistent $D\to 4$ Gauss-Bonnet gravity. Then, we study its thermodynamic ...properties near the critical point by employing new formalism of thermodynamic geometry (NTG). More precisely, critical exponents of the number density difference $\Delta n$, the isothermal compressibility ${{\kappa }_{T}}{{P}_{c}}$, the normalized intrinsic and the normalized extrinsic ${{K}_{N}}$ curvatures are calculated near the critical point for the small/large black holes phase. Our findings show that the critical amplitude of the normalized thermodynamic curvatures are independent of the Gauss-Bonnet coupling values that indicates their universal feature.
We use Clifford algebras to construct a unified formalism for studying constant extrinsic curvature immersed surfaces in Riemannian and semi-Riemannian 3-manifolds in terms of immersed bilegendrian ...surfaces in their unitary bundles. As an application, we provide full classifications of both complete and compact immersed bilegendrian surfaces in the unit tangent bundle
U
S
3
of the 3-sphere.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this paper, we study a conformally flat 3-space
which is an Euclidean 3-space with a conformally flat metric
with the conformal factor
, where
for
.
In particular, we construct all helicoidal ...surfaces in
by solving the second-order non-linear ODE with extrinsic curvature and
mean curvature functions. As a result, we give classification of minimal helicoidal surfaces as well as
examples for helicoidal surfaces with some extrinsic curvature and mean curvature functions in
In this paper we give a complete classification of simply connected homogeneous almost α-Kenmotsu three-manifolds M whose Ricci operator is invariant along the Reeb flow. We get this classification ...by using the Gaussian and the extrinsic curvature associated with the canonical foliation of M.
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IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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