Faruk F. Abi-Khuzam

A ONE-PARAMETER FAMILY OF MINIMAL SURFACES WITH FOUR PLANAR ENDS

Using Jacobian elliptic functions we construct a one-parameter family of regular complete minimal surfaces of genus one with total curvature – 16π and having four embedded planar ends. The explicit formulas obtained reveal that two ends are asymptotic to one and the same plane.

Hadamard convexity and multiplicity and location of zeros

We consider certain questions arising from a paper of Hayman concerning quantitative versions of the Hadamard three-circle theorem for entire functions. If b(r) denotes the second derivative of logM(r) with respect to log r, the principal contributions of this work are (i) a characterization of those entire f with nonnegative Maclaurin coefficients for which lim sup b(r) = 1 -4 and (ii) some exploration of the relationship between multiple zeros of f and the growth of b(r) .

Some recent geometric inequalities

FARUK F. ABI-KHUZAM studied under the supervision of Professor Albert Edrei at Syracuse University where he received his Ph.D. in 1975. He is now Professor of Mathematics at the American University of Beirut, Lebanon. He has held visiting positions at Cornell University (1975) and Syracuse University (1980). In 1987 he was selected a Fulbright Scholar and spent the Summer of 1987 as Honorary Fellow at the University of Wisconsin-Madison.

Inequalities and asymptotics for some moment integrals

For α>β−1>0

The star function for meromorphic functions of several complex variables

\alpha>\beta-1>0

Spherical Means Associated with Non-isotropic Dilation Groups

, we obtain two-sided inequalities for the moment integral I(α,β)=∫R|x|−β|sinx|αdx

On the growth of subharmonic functions in space

I(\alpha,\beta)=\int_{\mathbb{R}}|x|^{-\beta}|\sin x|^{\alpha}\,dx

Interpolation at Maximal Radii: A Characterization of the Binomial and Exponential Series

. These are then used to give the exact asymptotic behavior of the integral as α→∞

Fourier restriction to convex surfaces of revolution in R3

\alpha\rightarrow\infty

A TRIGONOMETRIC INEQUALITY AND ITS GEOMETRIC APPLICATIONS

. The case I(α,α)