3,542 research outputs found
Hyperbolic Alexandrov-Fenchel quermassintegral inequalities I
In this paper we prove the following geometric inequality in the hyperbolic
space \H^n (, which is a hyperbolic Alexandrov-Fenchel inequality,
\begin{array}{rcl} \ds \int_\Sigma \s_4 d \mu\ge \ds\vs
C_{n-1}^4\omega_{n-1}\left\{\left(\frac{|\Sigma|}{\omega_{n-1}} \right)^\frac
12 + \left(\frac{|\Sigma|}{\omega_{n-1}} \right)^{\frac 12\frac {n-5}{n-1}}
\right\}^2, \end{array} provided that is a horospherical convex
hypersurface. Equality holds if and only if is a geodesic sphere in
\H^n.Comment: 18page
A new mass for asymptotically flat manifolds
In this paper we introduce a mass for asymptotically flat manifolds by using
the Gauss-Bonnet curvature. We first prove that the mass is well-defined and is
a geometric invariant, if the Gauss-Bonnet curvature is integrable and the
decay order satisfies Then we show a positive
mass theorem for asymptotically flat graphs over . Moreover we
obtain also Penrose type inequalities in this case.Comment: 32 pages. arXiv:1211.7305 was integrated into this new version as an
applicatio
The Gauss-Bonnet-Chern mass of conformally flat manifolds
In this paper we show positive mass theorems and Penrose type inequalities
for the Gauss-Bonnet-Chern mass, which was introduced recently in \cite{GWW},
for asymptotically flat CF manifolds and its rigidity.Comment: 17 pages, references added, the statement of Prop. 4.6 correcte
The Large Deviation Principle and Steady-state Fluctuation Theorem for the Entropy Production Rate of a Stochastic Process in Magnetic Fields
Fluctuation theorem is one of the major achievements in the field of
nonequilibrium statistical mechanics during the past two decades. Steady-state
fluctuation theorem of sample entropy production rate in terms of large
deviation principle for diffusion processes have not been rigorously proved yet
due to technical difficulties. Here we give a proof for the steady-state
fluctuation theorem of a diffusion process in magnetic fields, with explicit
expressions of the free energy function and rate function. The proof is based
on the Karhunen-Lo\'{e}ve expansion of complex-valued Ornstein-Uhlenbeck
process
Strong cosmic censorship for the massless Dirac field in the Reissner-Nordstrom-de Sitter spacetime
We present the Fermi story of strong cosmic censorship in the near-extremal
Reissner-Nordstrom-de Sitter black hole. To this end, we first derive from
scratch the criterion for the quasi-normal modes of Dirac field to violate
strong cosmic censorship in such a background, which turns out to be exactly
the same as those for Bose fields, although the involved energy momentum tensor
is qualitatively different from that for Bose fields. Then to extract the
low-lying quasi-normal modes by Prony method, we apply Crank-Nicolson method to
evolve our Dirac field in the double null coordinates. As a result, it shows
that for a fixed near-extremal black hole, strong cosmic censorship can be
recovered by the black hole family mode once the charge of our
Dirac field is greater than some critical value, which is increased as one
approaches the extremal black hole.Comment: JHEP published versio
An optimization problem in virtual endoscopy
AbstractThis paper studies a graph optimization problem occurring in virtual endoscopy, which concerns finding the central path of a colon model created from helical computed tomography (CT) image data. The central path is an essential aid for navigating through complex anatomy such as colon. Recently, Ge et al. (1998) devised an efficient method for finding the central path of a colon. The method first generates colon data from a helical CT data volume by image segmentation. It then generates a 3D skeleton of the colon. In the ideal situation, namely, if the skeleton does not contain branches, the skeleton will be the desired central path. However, almost always the skeleton contains extra branches caused by holes in the colon model, which are artifacts produced during image segmentation. To remove false branches, Ge et al. (1998) formulated a graph optimization problem for obtaining the central path. This paper presents a refined formulation and justifies that the solution of the refined optimization problem represents the accurate central path of a colon. We then provide a fast algorithm for solving the problem
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