Nematic Films and Radially Anisotropic Delaunay Surfaces

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoid in addition to other new surfaces.Comment: 15 pages, 18 figure

On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines

We study transformations of coordinates on a Lorentzian Einstein manifold with a parallel distribution of null lines and show that the general Walker coordinates can be simplified. In these coordinates, the full Lorentzian Einstein equation is reduced to equations on a family of Einstein Riemannian metrics.Comment: Dedicated to Dmitri Vladimirovich Alekseevsky on his 70th birthda

Stability of complex hyperbolic space under curvature-normalized Ricci flow

Using the maximal regularity theory for quasilinear parabolic systems, we prove two stability results of complex hyperbolic space under the curvature-normalized Ricci flow in complex dimensions two and higher. The first result is on a closed manifold. The second result is on a complete noncompact manifold. To prove both results, we fully analyze the structure of the Lichnerowicz Laplacian on complex hyperbolic space. To prove the second result, we also define suitably weighted little H\"{o}lder spaces on a complete noncompact manifold and establish their interpolation properties.Comment: Some typos in version 2 are correcte

Bounding λ2 for Kähler–Einstein metrics with large symmetry groups

We calculate an upper bound for the second non-zero eigenvalue of the scalar Laplacian, λ2, for toric-Kähler–Einstein metrics in terms of the polytope data. We also give a similar upper bound for Koiso–Sakane type Kähler–Einstein metrics. We provide some detailed examples in complex dimensions 1, 2 and 3

The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ imposed by the contracted Codazzi equations. We use this fact to study the Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in B\"ar, Gauduchon, Moroianu (2005). We also answer negatively the corresponding questions in the smooth category.Comment: 28 pages; final versio

Evidence of the Purely Leptonic Decay B- --> tau- nu_tau-bar

We present the first evidence of the decay B- --> tau- nu_tau-bar using 414 fb^-1 of data collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. Events are tagged by fully reconstructing one of the B mesons in hadronic modes. We detect the signal with a significance of 3.5 standard deviations including systematics, and measure the branching fraction to be Br(B- --> tau- nu_tau-bar) = (1.79 +0.56-0.49(stat) +0.46-0.51(syst))*10^-4. This implies that f_B = 0.229 +0.036-0.031(stat) +0.034-0.037(syst) GeV and is the first direct measurement of this quantity.Comment: 6 pages, 3 figures, to appear in Physical Review Letter

Space-Time Diffusion of Ground and Its Fractal Nature

We present evidences of the diffusive motion of the ground and tunnels and show that if systematic movements are excluded then the remaining uncorrelated component of the motion obeys a characteristic fractal law with the displacement variance dY^2 scaling with time- and spatial intervals T and L as dY^2 \propto T^(Alpha)L^(Gamma) with both exponents close to 1. We briefly describe experimental methods of the mesa- and microscopic ground motion detection used in the measurements at the physics research facilities sensitive to the motion, particularly, large high energy elementary particle accelerators. A simple mathematical model of the fractal motion demonstrating the observed scaling law is also presented and discussed.Comment: 83 pages, 46 fig

Very Singular Diffusion Equations-Second and Fourth Order Problems

This paper studies singular diffusion equations whose diffusion effect is so strong that the speed of evolution becomes a nonlocal quantity. Typical examples include the total variation flow as well as crystalline flow which are formally of second order. This paper includes fourth order models which are less studied compared with second order models. A typical example of this model is an H−1 gradient flow of total variation. It turns out that such a flow is quite different from the second order total variation flow. For example, we prove that the solution may instantaneously develop jump discontinuity for the fourth order total variation flow by giving an explicit example

Observation of B0->pi0pi0

We report the first observation of the decay B0->pi0pi0, using a 253/fb data sample collected at the Upsilon(4S) resonance with the Belle detector at the KEKB e+e- collider. The measured branching fraction is BF(B0->pi0pi0) = {2.32 +0.4-0.5(stat) +0.2-0.3(syst)} x 10^-6, with a significance of 5.8 standard deviations including systematic uncertainties. We also make the first measurement of the direct CP violating asymmetry in this mode.Comment: 6 pages, 2 figures, submitted to ICHEP04, Beijing and Physical Review Letters. v2: a possible pile-up background is checked and a systematic error for it is include