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We prove that if a complete, properly embedded, finite-topology minimal surface in S2×R contains a line, then its ends are asymptotic to helicoids, and that if the surface is an annulus, it must be a helicoid.

No abstract uploaded!

No abstract uploaded!

The wave equation, ∂_{$tt$}$u$=Δ$u$, in ℝ^{$n$+1}, considered with initial data$u$($x$,0)=$f$∈$H$^{$s$}(ℝ^{$n$}) and$u$’($x$,0)=0, has a solution which we denote by $\frac{1}{2}(e^{it\sqrt{-\Delta}}f+e^{-it\sqrt{-\Delta}}f)$ . We give almost sharp conditions under which $\sup_{0<t<1}|e^{\pm it\sqrt{-\Delta}}f|$ and $\sup_{t\in\mathbb{R}}|e^{\pm it\sqrt{-\Delta}}f|$ are bounded from$H$^{$s$}(ℝ^{$n$}) to$L$^{$q$}(ℝ^{$n$}).

We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.

No abstract uploaded!

No abstract uploaded!

We study weakly trapped submanifolds of codimension two in a standard static spacetime. In this setting, we apply some generalized maximum principles in order to investigate the geometry of these trapped submanifolds. For instance, we establish sufficient conditions to guarantee that such a spacelike submanifold must be a hypersurface of the Riemannian base of the ambient spacetime. As a consequence, we prove that there do not exist n-dimensional compact (without boundary) trapped submanifolds immersed in an (n+2)-dimensional standard static spacetime. Such a nonexistence result was originally obtained for stationary spacetimes by Mars and Senovilla [20]. Furthermore, we also investigate parabolic weakly trapped submanifolds immersed in a standard static spacetime.

The aim of this paper is to give a proof of the calculation of the flabby class group of a finite cyclic group due to Endo and Miyata [2]. In the next section I will recall the definition and some basic facts about this group. In the final section I will give some examples to show that the invertibility conditions used by Endo and Miyata cannot be removed. I would like to thank M.c. Kang for useful comments and for showing me his results on some related problems.

In this paper, it is proved that the Hodge metric completion of the moduli space of polarized and marked Calabi-Yau manifolds, ie the Torelli space, is a complex affine manifold. As applications we prove that the period map from the Torelli space and the extended period map from its completion space, both are injective into the period domain, and that the completion space is a bounded domain of holomorphy with a complete Khler-Einstein metric. As a corollary we show that the period map from the moduli space of polarized Calabi-Yau manifolds with level m structure is also injective.

For the steady-state solution of an integraldifferential equation from a two-dimensional model in transport theory, we shall derive and study a nonsymmetric algebraic Riccati equation B--XF--F+ X+ XB+ X= 0, where F I-s PD, B-(b I+ s P) D-and B+ b I+ s PD+ with a nonnegative matrix P, positive diagonal matrices D, and nonnegative parameters f, b b/(1-f) and s s/(1-f). We prove the existence of the minimal nonnegative solution X under the physically reasonable assumption f+ b+ s P (D++ D-)&lt; 1, and study its numerical computation by fixed-point iteration, Newtons method and doubling. We shall also study several special cases; eg when b = 0 and P is low-ranked, then X= s 2 UV is low-ranked and can be computed using more efficient iterative processes in U and V. Numerical examples will be given to illustrate our theoretical results.

In this paper we generalize a result in [J. An, Z. Wang, On the realization of Riemannian symmetric spaces in Lie groups, Topology Appl. 153 (7) (2005) 10081015, showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of fixed points of involutions are also proved.

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No abstract uploaded!

An almost K\"ahler structure on a symplectic manifold (N,ω) consists of a Riemannian metric g and an almost complex structure J such that the symplectic form ω satisfies ω(⋅,⋅)=g(J(⋅),⋅) . Any symplectic manifold admits an almost K\"ahler structure and we refer to (N,ω,g,J) as an almost K\"ahler manifold. In this article, we propose a natural evolution equation to investigate the deformation of Lagrangian submanifolds in almost K\"ahler manifolds. A metric and complex connection $\hn$ on TN defines a generalized mean curvature vector field along any Lagrangian submanifold M of N . We study the evolution of M along this vector field, which turns out to be a Lagrangian deformation, as long as the connection $\hn$ satisfies an Einstein condition. This can be viewed as a generalization of the classical Lagrangian mean curvature flow in K\"ahler-Einstein manifolds where the connection $\hn$ is the Levi-Civita connection of g . Our result applies to the important case of Lagrangian submanifolds in a cotangent bundle equipped with the canonical almost K\"ahler structure and to other generalization of Lagrangian mean curvature flows, such as the flow considered by Behrndt \cite{b} in K\"ahler manifolds that are almost Einstein.

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No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

In this ar ti cle, the authors de vel oped an al ter na tive meth od ol ogy to cal cu late theoption- adjusted spread for the mortgage- backed se cu ri ties us ing par tial dif fer ential equa tion tech nique. The nu meri cal im ple men ta tion is dis cussed in de tail, includ ing the con ver gence and er ror analy sis. This ap proach pro vides us a fast andac cu rate way to pric ing MBS.

In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and nonstationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently developed compressed (compressive) sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form {a(t) cos(θ(t))}, where a ∈ V (θ), V (θ) consists of the functions smoother than cos(θ(t)) and θ   0. This problem can be formulated as a nonlinear l0 optimization problem. In order to solve this optimization problem, we propose a nonlinear matching pursuit method by generalizing the classical matching pursuit for the l0 optimization problem. One important advantage of this nonlinear matching pursuit method is it can be implemented very efficiently and is very stable to noise. Further, we provide an error analysis of our nonlinear matching pursuit method under certain scale separation assumptions. Extensive numerical examples will be given to demonstrate the robustness of our method and comparison will be made with the state-of-the-art methods. We also apply our method to study data without scale separation, and data with incomplete or under-sampled data.

We prove we can build (transitive or nontransitive) Anosov flows on closed three-dimensional manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications of this result; for example: 1.We build a closed three-dimensional manifold supporting both a transitive Anosov vector field and a nontransitive Anosov vector field. 2.For any n, we build a closed three-dimensional manifold M supporting at least n pairwise different Anosov vector fields. 3.We build transitive hyperbolic attractors with prescribed entrance foliation; in particular, we construct some incoherent transitive hyperbolic attractors. 4.We build a transitive Anosov vector field admitting infinitely many pairwise nonisotopic transverse tori.