937 research outputs found
Curvature estimates for submanifolds in warped products
We give estimates on the intrinsic and the extrinsic curvature of manifolds
that are isometrically immersed as cylindrically bounded submanifolds of warped
products. We also address extensions of the results in the case of submanifolds
of the total space of a Riemannian submersion.Comment: 21 page
Eigenvalue estimates for submanifolds of warped product spaces
We give lower bounds for the fundamental tone of open sets in minimal
submanifolds immersed into warped product spaces of type ,
where . We also study the essential spectrum of these
minimal submanifolds.Comment: 17 page
Quantum statistical correlations in thermal field theories: boundary effective theory
We show that the one-loop effective action at finite temperature for a scalar
field with quartic interaction has the same renormalized expression as at zero
temperature if written in terms of a certain classical field , and if
we trade free propagators at zero temperature for their finite-temperature
counterparts. The result follows if we write the partition function as an
integral over field eigenstates (boundary fields) of the density matrix element
in the functional Schr\"{o}dinger field-representation, and perform a
semiclassical expansion in two steps: first, we integrate around the
saddle-point for fixed boundary fields, which is the classical field ,
a functional of the boundary fields; then, we perform a saddle-point
integration over the boundary fields, whose correlations characterize the
thermal properties of the system. This procedure provides a
dimensionally-reduced effective theory for the thermal system. We calculate the
two-point correlation as an example.Comment: 13 pages, 1 figur
Gravitational lensing in a universe with matter and a cosmological constant
We extend the results obtained in previous works by Piattella and Park for gravitational lensing in the McVittie metric by including the effect of the transition from the matter-dominated epoch of the Universe to the
Λ
-dominated era. We derive a formula that agrees with the previous results for the McVittie metric at lowest order and compare the lensing angle predictions obtained from the Schwarzschild approximation, the McVittie model, and higher order corrections to the McVittie model. In doing this, we test if, beyond the correction from the accelerated expansion of the Universe, there is a need for including the matter content of the Universe in modeling lens systems at the redshifts observed in lens systems. We investigate if there is a need for a modification of the lens equation from these corrections and, if so, to which order and whether it is measurable. We find that, while the effect is of the same order as the one calculated previously, there is no significant contribution to the bending angle, as the first order effect is already of order
O
(
θ
4
O
)
in the observed angle
Foliations and Chern-Heinz inequalities
We extend the Chern-Heinz inequalities about mean curvature and scalar
curvature of graphs of -functions to leaves of transversally oriented
codimension one -foliations of Riemannian manifolds. That extends
partially Salavessa's work on mean curvature of graphs and generalize results
of Barbosa-Kenmotsu-Oshikiri \cite{barbosa-kenmotsu-Oshikiri} and
Barbosa-Gomes-Silveira \cite{barbosa-gomes-silveira} about foliations of
3-dimensional Riemannian manifolds by constant mean curvature surfaces. These
Chern-Heinz inequalities for foliations can be applied to prove
Haymann-Makai-Osserman inequality (lower bounds of the fundamental tones of
bounded open subsets in terms of its inradius)
for embedded tubular neighborhoods of simple curves of .Comment: This paper is an improvment of an earlier paper titled On Chern-Heinz
Inequalities. 8 Pages, Late
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