关于Lapleca算子的大特征值

在两种情下，给出了Laplace算子大特征值的的上界估计，改进了两个已有的结果。     

Control of integral manifolds loosing their attractivity in time

The work is devoted to the investigation of the integral manifolds of the nonautonomous slow-fast systems, which change their attractivity in time. The method used here is based on gluing attracting and repelling integral manifolds by using an additional control function.     

Isolated complex singularities and their CR links Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information from its link. We also give some open problems to be further pursued.     

Yang—Mills流演化问题奇点集的估计

给出了Ｙａｎｇ－Ｍｉｌｌｓ流演化问题奇点集的一个估计。     

On harmonic and asymptotically harmonic homogeneous spaces

We classify noncompact homogeneous spaces which are Einstein and asymptotically harmonic. This completes the classification of Riemannian harmonic spaces in the homogeneous case: Any simply connected homogeneous harmonic space is flat, or rank-one symmetric, or a nonsymmetric Damek–Ricci space. Independently, Y. Nikolayevsky has obtained the latter classification under the additional assumption of nonpositive sectional curvatures [N2]. Supported in part by DFG priority program “Global Differential Geometry” (SPP 1154). Received: September 2004; Revision: June 2005; Accepted: September 2005     

An index theorem for Toeplitz operators on odd-dimensional manifolds with boundary

We establish an index theorem for Toeplitz operators on odd-dimensional spin manifolds with boundary. It may be thought of as an odd-dimensional analogue of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. In particular, there occurs naturally an invariant of η type associated to K¹ representatives on even-dimensional manifolds, which should be of independent interests. For example, it gives an intrinsic interpretation of the so called Wess-Zumino term in the WZW theory in physics.     

Moving Symplectic Curves in Kähler-Einstein Surfaces

We derive a parabolic equation for the K?hler angle of a real surface evolving under the mean curvature flow in a K?hler-Einstein surface and show that a symplectic curve remains symplectic with the flow. Received March 29, 2000, Revised April 29, 2000, Accepted May 16, 2000     

Linearization-preserving self-adjoint and symplectic integrators

This article is concerned with geometric integrators which are linearization-preserving, i.e. numerical integrators which preserve the exact linearization at every fixed point of an arbitrary system of ODEs. For a canonical Hamiltonian system, we propose a new symplectic and self-adjoint B-series method which is also linearization-preserving. In a similar fashion, we show that it is possible to construct a self-adjoint and linearization-preserving B-series method for an arbitrary system of ODEs. Some numerical experiments on Hamiltonian ODEs are presented to test the behaviour of both proposed methods. This work was supported by the Australian Research Council and by the Marsden Fund of the Royal Society of New Zealand.