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 $(1,1)$ 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 B→DKKB \to DKK decays

A study of hadron pair production mechanism is motivated by the recent observed decays $\bar B^0\to D^{(*)+}K^-K^0$. 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 $\bar B^0\to D^{(*)+}K^-K^0$ 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 $n$, 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