30,590 research outputs found
Comparison and Rigidity Theorems in Semi-Riemannian Geometry
The comparison theory for the Riccati equation satisfied by the shape
operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds
of arbitrary index, using one-sided bounds on the Riemann tensor which in the
Riemannian case correspond to one-sided bounds on the sectional curvatures.
Starting from 2-dimensional rigidity results and using an inductive technique,
a new class of gap-type rigidity theorems is proved for semi-Riemannian
manifolds of arbitrary index, generalizing those first given by Gromov and
Greene-Wu. As applications we prove rigidity results for semi-Riemannian
manifolds with simply connected ends of constant curvature.Comment: 46 pages, amsart, to appear in Comm. Anal. Geo
String Effects on Fermi--Dirac Correlation Measurements
We investigate some recent measurements of Fermi--Dirac correlations by the
LEP collaborations indicating surprisingly small source radii for the
production of baryons in -annihilation at the peak. In the
hadronization models there are besides the Fermi--Dirac correlation effect also
a strong dynamical (anti-)correlation. We demonstrate that the extraction of
the pure FD effect is highly dependent on a realistic Monte Carlo event
generator, both for separation of those dynamical correlations which are not
related to Fermi--Dirac statistics, and for corrections of the data and
background subtractions. Although the model can be tuned to well reproduce
single particle distributions, there are large model-uncertainties when it
comes to correlations between identical baryons. We therefore, unfortunately,
have to conclude that it is at present not possible to make any firm conclusion
about the source radii relevant for baryon production at LEP
A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry
The strong maximum principle is proved to hold for weak (in the sense of
support functions) sub- and super-solutions to a class of quasi-linear elliptic
equations that includes the mean curvature equation for spacelike
hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped
product splitting theorem is given.Comment: 37 pages, 1 figure, ams-latex using eepi
A Relativistic Mean Field Model for Entrainment in General Relativistic Superfluid Neutron Stars
General relativistic superfluid neutron stars have a significantly more
intricate dynamics than their ordinary fluid counterparts. Superfluidity allows
different superfluid (and superconducting) species of particles to have
independent fluid flows, a consequence of which is that the fluid equations of
motion contain as many fluid element velocities as superfluid species. Whenever
the particles of one superfluid interact with those of another, the momentum of
each superfluid will be a linear combination of both superfluid velocities.
This leads to the so-called entrainment effect whereby the motion of one
superfluid will induce a momentum in the other superfluid. We have constructed
a fully relativistic model for entrainment between superfluid neutrons and
superconducting protons using a relativistic mean field model
for the nucleons and their interactions. In this context there are two notions
of ``relativistic'': relativistic motion of the individual nucleons with
respect to a local region of the star (i.e. a fluid element containing, say, an
Avogadro's number of particles), and the motion of fluid elements with respect
to the rest of the star. While it is the case that the fluid elements will
typically maintain average speeds at a fraction of that of light, the
supranuclear densities in the core of a neutron star can make the nucleons
themselves have quite high average speeds within each fluid element. The
formalism is applied to the problem of slowly-rotating superfluid neutron star
configurations, a distinguishing characteristic being that the neutrons can
rotate at a rate different from that of the protons.Comment: 16 pages, 5 figures, submitted to PR
Corona-type theorems and division in some function algebras on planar domains
Let be an algebra of bounded smooth functions on the interior of a
compact set in the plane. We study the following problem: if
satisfy , does there exist
and a constant such that ? A
prominent role in our proofs is played by a new space, C_{\dbar, 1}(K), which
we call the algebra of \dbar-smooth functions.
In the case , a complete solution is given for the algebras of
functions holomorphic in and whose first -derivatives extend
continuously to \ov{K^\circ}. This necessitates the introduction of a special
class of compacta, the so-called locally L-connected sets.
We also present another constructive proof of the Nullstellensatz for ,
that is only based on elementary \dbar-calculus and Wolff's method.Comment: 23 pages, 6 figure
Blowup of Jang's equation at outermost marginally trapped surfaces
The aim of this paper is to collect some facts about the blowup of Jang's
equation. First, we discuss how to construct solutions that blow up at an
outermost MOTS. Second, we exclude the possibility that there are extra blowup
surfaces in data sets with non-positive mean curvature. Then we investigate the
rate of convergence of the blowup to a cylinder near a strictly stable MOTS and
show exponential convergence near a strictly stable MOTS.Comment: 15 pages. This revision corrects some typo
Maximum fidelity retransmission of mirror symmetric qubit states
In this paper we address the problem of optimal reconstruction of a quantum state from the result of a single measurement when the original quantum state is known to be a member of some specified set. A suitable figure of merit for this process is the fidelity, which is the probability that the state we construct on the basis of the measurement result is found by a subsequent test to match the original state. We consider the maximisation of the fidelity for a set of three mirror symmetric qubit states. In contrast to previous examples, we find that the strategy which minimises the probability of erroneously identifying the state does not generally maximise the fidelity
- …