21,955 research outputs found
The Chern-Ricci flow on Oeljeklaus-Toma manifolds
We study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on
a family of Oeljeklaus-Toma (OT-) manifolds which are non-K\"{a}hler compact
complex manifolds with negative Kodaira dimension. We prove that, after an
initial conformal change, the flow converges, in the Gromov-Hausdorff sense, to
a torus with a flat Riemannian metric determined by the OT-manifolds
themselves.Comment: 22pages,correct some typo
An almost complex Chern-Ricci flow
We consider the evolution of an almost Hermitian metric by the part
of its Chern-Ricci form on almost complex manifolds. This is an evolution
equation first studied by Chu and coincides with the Chern-Ricci flow if the
complex structure is integrable and with the K\"ahler-Ricci flow if moreover
the initial metric is K\"ahler. We find the maximal existence time for the flow
in term of the initial data and also give some convergence results. As an
example, we study this flow on the (locally) homogeneous manifolds in more
detail.Comment: 28pages, the final version accepted by The Journal of Geometric
Analysi
The factorization in exclusive B decays: a critical look
I review the theoretical ideas and concepts along the line of factorization
in the exclusive B decays. In order to understand the naive factorization, the
effective field theories and the perturbative method of QCD are introduced and
developed. We focus our discussions on the large energy effective theory, the
QCD factorization approach and the soft-collinear effective theory.Comment: Talk at (or Contribution to) the International Workshop on QCD:
QCD@Work 2003 - Conversano (Italy) 14-18 June 2003 (eConf C030614). 6 page
The QCD factorization in decays
A study of hadron pair production mechanism is motivated by the recent
observed decays . One novel phenomenon is threshold
enhancement of the kaon pair production. We show that these decays in the heavy
quark mass limit can be factorized into a generalized form. The new
non-perturbative quantity is the generalized distribution amplitude which
describes how a quark-antiquark pair transmits into the hadron pair. A proof of
factorization of decays to all-orders is performed
by using the soft-collinear effective theory. The phenomenological application
is discussed in brief.Comment: 14 pages, 2 figure
Sudakov form factor in effective field theory
We discuss the Sudakov form factor in the framework of the soft-collinear
effective theory. The running of the short distance coefficient function from
high to low scale gives the summation of Sudakov logarithms to all orders. Our
discussions concentrate on the factorization and derivation of the
renormalization group equation from the effective theory point of view. The
intuitive interpretation of the renormalization group method is discussed. We
compared our method with other resummation approaches in the literatures.Comment: 27 pages, 7 figures, revtex
An upper bound of the heat kernel along the harmonic-Ricci flow
In this paper, we first derive a Sobolev inequality along the harmonic-Ricci
flow. We then prove a linear parabolic estimate based on the Sobolev inequality
and Moser's iteration. As an application, we will obtain an upper bound
estimate for the heat kernel under the flow.Comment: 16pages. arXiv admin note: text overlap with arXiv:1412.3200 by other
author
The (logarithmic) Sobolev inequalities along geometric flow and applications
For some class of geometric flows, we obtain the (logarithmic) Sobolev
inequalities and their equivalence up to different factors directly and also
obtain the long time non-collapsing and non-inflated properties, which
generalize the results in the case of Ricci flow or List-Ricci flow or
harmonic-Ricci flow. As applications, for mean curvature flow in Lorentzian
space with nonnegative sectional curvature and twisted K\"ahler-Ricci flow on
Fano manifolds, we get the results above.Comment: 35pages,correct some typo
Isoperimetric inequality along the twisted K\"{a}hler-Ricci flow
We prove a uniform isoperimetric inequality for all time along the twisted
K\"{a}hler-Ricci flow on Fano manifolds.Comment: 12 pages, accepted by Differential Geometry and its Application
Transverse Fully Nonlinear Equations on Sasakian Manifolds and Applications
We prove a priori estimates for a class of transverse fully nonlinear
equations on Sasakian manifolds and give some geometric applications such as
the transversion Calabi-Yau theorem for transverse balanced and (strongly)
Gauduchon metrics. We also explain that similar results hold on compact
oriented, taut, transverse Hermitian foliated manifold of complex co-dimension
, and give some geometric applications such as the transverse Calabi-Yau
theorems for transverse Hermitian and (strongly) Gauduchon metrics.Comment: 46 pages,minor typos correction,final version to appear in Advances
in Mathematic
Magnetized Gas Collimation of Interstellar Outflow Scaled by Laser-produced Plasma
Young stellar objects/planetary nebula outflow anisotropies usually involve
wind-wind interactions and magnetic collimation, but detailed structures of
wind and magnetic fields inside collimation region remain undetermined. We
numerically investigated its laboratory counterpart, based on poloidal field
collimation in magnetocentrifugal launching model. Our analog consist of fast
wind: Aluminum plasma generated by laser and magnetized ambient: molecular
Helium and B=5-60 Tesla embedded field. Elevating magnetic field strength or
decreasing gas density can alter expansion morphology, from sphere to prolonged
cavity and ultimately to collimated jet. Outflow patterns can be quantitatively
predicted based on the knowledge of its surroundings through a set of external
Mach numbers. We conclude that such mixed gas and magnetic field dynamics are
consistent with astronomical observations of protostars and planetary nebulae
in certain evolution stages, and here provide a scalable framework allowing
fitting of flow-field structures in astronomical unresolved regions by assuming
their possible geometries on a repeatable laboratory platform.Comment: 18 pages with 7 figures and 1 tabl
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