Daowei Ma

A hopf lemma for holomorphic functions and applications

A new boundary uniqueness result for holomorphic functions is obtained. Applications are provided.

Optimal Lp estimates for the\(\bar \partial \)-equation on complex ellipsoids in ℂn-equation on complex ellipsoids in ℂn

AbstractIn this paper we prove the best possible Lp estimates for the

Smoothness of kobayashi metric of ellipsoids

\bar \partial

PERTURBATION OF DOMAINS AND AUTOMORPHISM GROUPS

-equation on complex ellipsoids in ℂn, and provide examples to show why they cannot be improved.

Numerical Harmonic Analysis on the Hyperbolic Plane

The equations which model the elastostatic shallow circular cylindrical shell (see, e.g., [6,15,23,29]) constitute an important elliptic partial differential equation (PDE) system in the study of shell structures. When the system is subjected to a concentrated point load, the response is described by a fundamental solution of the PDE system. We have found some mathematical inconsistencies in the existing literature. Therefore, in this paper, we discuss these errors, then we use partial fractions and Fourier transform techniques to determine the fundamental solution. Explicit expressions in terms of special functions and convolution integrals are derived and simplified so that the formulas are suitable for algorithmic evaluation and for application elsewhere.

Spectra of unitary integral operators on L-2 (R) with kernels k(xy)

Lempert proved that the Kobayashi metric and the Caratheodory metric of smooth strongly convex domains are smooth away from the zero section of the holomorphic tangent bundle. We will show that if the strong convexity is replaced by the weaker condition of strict convexity the above smoothness result is no longer valid even if the boundary is real analytic. We study the smoothness of the Kobayashi metric of ellipsoids. We prove that the Kobayashi metric of domains of the form , where m≥3/2, is piecewise C 3 off the zero section, but not C 3.

The Euler-Bernoulli Beam Equation with Boundary Energy Dissipation.

We study the fixed point sets of holomorphic self- maps of a bounded domain in C n . Specifically we investigate the least number of fixed points in general position in the domain that forces any automorphism (or endomorphism) to be the identity. We have discovered that in terms of this number one can give the necessary and sufficient condition for the domain to be biholomor- phic to the unit ball. Other theorems and examples generalize and complete previous results in this area, especially the recent work of Jean-Pierre Vigue.

The Kobayashi metric of a complex ellipsoid in {

The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in C n under small perturbation of this domain in the Hausdorff metric. We consider a number of examples when an arbitrary small perturbation can lead to a domain with a larger group, present theorems concerning upper semicontinuity property of some invariants of automorphism groups. We also prove that the dimension of an abelian subgroup of the automorphism group of a bounded domain in C n does not exceed n.