A minimizing deformation of Legendrian submanifolds in the standard sphere

In this note we study the moduli space of minimal Legendrian submanifolds in the standard sphere S²ⁿ⁻¹. We show that new examples of minimal Legendrian submanifolds can be constructed, if we can solve a certain equation for a function on a nearby glued Legendrian submanifold. As a step toward solving this equation, we prove short-time existence for a particular gradient flow on the space of immersed Legendrian submanifolds. A new necessary condition for a Lagrangian embedding into is given.     

Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps

Let be a nonempty closed convex subset of a real Banach space and be a Lipschitz pseudocontractive self-map of with . An iterative sequence is constructed for which as . If, in addition, is assumed to be bounded, this conclusion still holds without the requirement that Moreover, if, in addition, has a uniformly Gâteaux differentiable norm and is such that every closed bounded convex subset of has the fixed point property for nonexpansive self-mappings, then the sequence converges strongly to a fixed point of . Our iteration method is of independent interest.

     

Norm inequalities of periodic functions and their derivatives

If v is a function on [0,1] such that v^(j) is absolutely continuous and $v^{(j)}(0) + v^{(j)}(1) = 0$ for $0 \leq j \leq n-1$, the inequality in L^p norm between v and the derivative v⁽ⁿ⁾ is proved if $v^{(n)} \in L^{p}[0,1]$, and is shown by examples to be best possible when p = 1, 2 and $\infty$. The method of proof relies on the explicit form of the Green functions of some boundary value problems obtained recently and is applied to refine some related inequalities by J. Favard and D. G. Northcott. Received: 26 April 2002     

Extension and lifting of polynomials

We characterize the Banach spaces enjoying polynomial lifting properties, and the spaces that admit compact extensions of polynomials.Received: 20 June 2002     

The modular automorphisms of the Drinfeld modular curve $$ X_{1}(\frak n) $$

In this work we determine the group of modular automorphisms of the Drinfeld modular curve for any nonconstant polynomial .Received: 19 September 2002     

Composite Julia sets generated by infinite polynomial arrays

A definition of a generalized filled-in Julia set generated by an infinite array of proper polynomial mappings in  is introduced. It is shown that such Julia sets depend analytically on the defining polynomial mappings.     

Axiomatic homotopy theory for operads

We give sufficient conditions for the existence of a model structure on operads in an arbitrary symmetric monoidal model category. General invariance properties for homotopy algebras over operads are deduced.     

On algebras of two dimensional singular integral operators with homogeneous discontinuities in symbols

We describe the Fredholm symbol algebra for theC ^*-algebra generated by two dimensional singular integral operators, acting onL ₂(²), and whose symbols admit homogeneous discontinuities. Locally these discontinuities are modeled by homogeneous functions having slowly oscillating (and, in particular, piecewise continuous) discontinuities on a system of rays outgoing from the origin.These results extend the well-known Plamenevsky results for the two dimensional case. We present here an alternative and much clearer approach to the problem.Rostov State University RussiaPartially supported by Russian Fund for Fundamental Investigations, RFFI-98-01-01-023, and by CONACYT project 32424-EPartially supported by CONACYT Project 27934-E, México.     

A trace formula for Weyl transforms with radial symbols

A trace formula for Weyl transforms onL ² () with radial symbols is given.This research has been partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0008562.     

Smallest g -supersolution with constraint

In this paper the existence and uniqueness of the smallest g-supersolution for BSDE is discussed in the case without Lipschitz condition imposing on both constraint function and drift coefficient in the different method from the one with Lipschitz condition. Then by considering (ξ, g) as a parameter of BSDE, and (ξ ^α, g ^α) as a class of parameters for BSDE, where α belongs to a set , for every there exists a pair of solution {Y ^a, Z^a} for the BSDE, the properties of which is also a solution for some BSDE is studied. This result may be used to discuss optimal problems with recursive utility. This work was supported by NSFC (79790130)