A Model with Exact Inflationary Solution in Finsler Universe

In this paper, using the Gravity’s Rainbow theory, we introduce rainbow metric into rainbow Robertson-Walker metric, and obtain a model which depends on the energy of probe particles. Furthermore, we research on an exact inflationary solution of the model, and it can be consistent with the conclusions of observation. The results of our research show that some details in inflation depend on the energy of particles which are observed by observers.     

The Weil–Petersson Isometry Group

We prove that, for 3g–3+n>1 and (g,n)(1,2), the group of Weil–Petersson isometries of the Teichmüller space T _g,n coincides with the extended mapping class group.     

On Short Time Asymptotic Behavior of Some Symmetric Diffusions on General State Spaces

For conservative symmetric diffusions on a general state space (X,m), the short time asymptotic behavior of tlog _X 1 _A T _t 1 _B dm is investigated, where T _t is the associated semigroup and A and B are measurable subsets of X. It is proved that the superior limit is dominated by the inferior limit up to some absolute constant. When ₂ of the associated Dirichlet form is lower bounded, it is shown that the limit exists for any A and B, and is described by the intrinsic metric between them. Applications to infinite-dimensional spaces and fractals are given.     

Chaos in Black Holes Surrounded by Electromagnetic Fields

In this paper we study the occurrence of chaos for charged particles moving around a Schwarzschild black hole, perturbed by uniform electric and magnetic fields. The appearance of chaos is analyzed resorting to the Poincaré-Melnikov method.     

Brane Cosmology, Varying Speed of Light and Inflation in Models with One or More Extra Dimensions

We summarize the approach to brane cosmology known as mirage cosmology and use it to determine the Friedmann equation on a 3-brane embedded in different bulk spacetimes all with one or more extra dimensions. Usually, when there is more than one extra dimension the junction conditions, central to the usual brane world scenarios, are difficult to apply. This problem does not arise in mirage cosmology because the brane is treated as a test particle in the background spacetime. We discuss in detail the dynamics of a brane embedded in two specific 10D bulk spacetimes, namely Sch-AdS₅ × S₅ and a rotating black hole, and from the dynamics—which are now rather more complicated since the brane can move in all the extra dimensions—determine the new dark fluid terms in the brane Friedmann equation. Some of these, such as the cosmological constant term, are seen to be bulk dependent. We then show explicitly how this mirage cosmology approach matches with the familiar junction condition approach when there is just one extra dimension. The issue of a varying speed of light in mirage cosmology is addressed and we find a scenario in which c _eff always increases, tending asymptotically to c ₀ as the universe expands. Finally some comments are made regarding brane inflation and limitations of the mirage cosmology approach are also discussed.     

Bergman kernel and metric on non-smooth pseudoconvex domains

A stability theorem of the Bergman kernel and completeness of the Bergman metric have been proved on a type of non-smooth pseudoconvex domains defined in the following way:D = {z∈U|r(z)} <whereU is a neighbourhood of andr is a continuous plurisubharmonic function onU. A continuity principle of the Bergman Kernel for pseudoconvex domains with Lipschitz boundary is also given, which answers a problem of Boas.     

Integrability of superharmonic functions, uniform domains, and Hölder domains

Let denote the space of all positive superharmonic functions on a domain . Lindqvist showed that is a bounded subset of . Using this, we give a characterization of finitely connected -dimensional uniform domains and remarks on Hölder domains.

     

On Extensive Subsets of Convex Bodies

A subset S of a d-dimensional convex body K is extensive if S ∂K and for any p, q ∈ S the distance between p and q is at least one-half of the maximum length of chords of K parallel to the segment pq. In this paper we establish the general upper bound |S| ≤ 3 ^d — 1. We also find an upper bound for a certain class of 3-polytopes, which leads to the determination of the maximum cardinalities of extensive subsets and their extremal configurations for tetrahedra, octahedra and some other 3-polytopes. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the Diameter of Plane Curves

Recently, differential geometric properties of embedded projective varieties have gained increasing interest. In this note, we consider plane algebraic curves equipped with the Fubini--Study metric from₂ () and give an estimate for the diameter in terms of the degree, initiated in a paper by F. A. Bogomolov.     

On lower bounds for theL 2-Wasserstein metric in a Hilbert space

We provide two families of lower bounds for theL ²-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02.