1.
Growth estimates for logarithmic derivatives of Blaschke products and of functions in the Nevanlinna class - Heittokangas, Janne
We prove growth estimates for logarithmic derivatives of functions in the Nevanlinna class. Blaschke products with radially restricted zero sequences will be of particular interest. Our results are sharper in a certain sense than the corresponding estimates in [2] obtained for meromorphic functions in the unit disc.
2.
Domains of variability of Laurent coefficients and the convex hull for the family of concave univalent functions - Bhowmik, Bappaditya; Ponnusamy, Saminathan; Wirths, Karl-Joachim
Let D denote the open unit disc and let p $\in$ (0,1). We consider the family Co(p) of functions f : D ? $\overline{{\mathbf C}}$ that satisfy the following conditions: ¶ (i) f is meromorphic in D and has a simple pole at the point p. ¶ (ii) f(0) = f?(0) 1 = 0. ¶ (iii) f maps D conformally onto a set whose complement with respect to $\overline{{\mathbf C}}$ is convex. ¶ We determine the exact domains of variability of some coefficients an (f) of the Laurent expansion ¶ $f(z)=\sum_{n=-1}^{\infty} a_n(f)(z-p)^n,$ |z p|<1 p, ¶ for...
4.
On the existence of spherically bent submanifolds,\\an analogue of a theorem of E.\,Cartan - Pawel, Knut; Reckziegel, Helmut
In this article an analogue of E.\,Cartan's theorem about the existence of (local) totally geodesic sub\-mani\-folds with a prescribed tangent plane is proved, namely for the existence of spherically bent submanifolds (= extrinsic spheres); also a global version is deduced.
5.
Reducible hyperplane sections, II. - Beltrametti, M.C.; Chandler, K.A.; Sommese, A.J.
Let $\hatX$ be a smooth connected subvariety of complex projective
space $\pn n$. The question was raised in \cite{CHS} of how to
characterize $\hatX$ if it admits a reducible hyperplane
section $\hatL$. In the case in which $\hatL$ is
the union of $r \geq 2$ smooth normal crossing divisors, each of
sectional genus zero, classification theorems were given for
$\dim \hatX \geq 5$ or $\dim X=4$ and $r=2$.
This paper restricts attention to the case of two divisors on a
threefold, whose sum is ample, and which meet transversely in a
smooth curve of genus at least $2$. A finiteness theorem and some
general results are proven, when the two...
6.
Uniqueness of entire functions and fixed points - Chang, Jianming; Fang, Mingliang
Let $f$ be a nonconstant entire function.
%If $f(z)=z$ $\Longleftrightarrow $ $f'(z)=z$, and
%$f'(z)=z$ $\Longrightarrow $ $f''(z)=z$, then $f\equiv f'$. In particular,
If $f$, $f'$ and $f''$ have the same fixed points, then $f\equiv f'.$
7.
Entire functions that share a polynomial with one of their derivatives - Wang, Jian-ping
In this paper, we investigate the entire functions
that share a polynomial with one of their derivatives and prove
several theorems which generalize the main results given by L. Z.
Yang in [14].
8.
Isospectral hypersurfaces in Euclidean spheres - Barbosa, Jos\'e N. B.
The aim of this work is to present a classification of some compact hypersurfaces $M^{n}$ of a unit sphere $S^{n+1}$ provided the spectra of the Laplacian of $p$-forms of $M^{n}$, which we denote by $\mathrm{Spec}^p(M)$, is equal to the spectra $\mathrm{Spec}^p(M_0)$, of a given hypersurface $M_{0}^{n}$.
10.
Curvature-adapted real hypersurfaces in quaternionic space forms - Adachi, Toshiaki; Maeda, Sadahiro
In this paper we study geodesics on curvature-adapted real hypersurfaces in non-flat quaternionic space forms. By observing the extrinsic shape of geodesics on these hypersurfaces we characterize them in the class of real hypersurfaces. We also investigate the length spectrum of geodesic spheres, which are the simplest curvature-adapted real hypersurfaces, in non-flat quaternionic space forms.
14.
A remark on universal coverings of holomorphic families of Riemann surfaces - Imayoshi, Yoichi; Nishimura, Minori
We study the universal covering space $\tilde M$ of a holomorphic family (M, ?, R) of Riemann surfaces over a Riemann surface R. The main result is that (1) $\tilde M$ is topologically equivalent to a two-dimensional cell, (2) $\tilde M$ is analytically equivalent to a bounded domain in C2, (3) $\tilde M$ is not analytically equivalent to the two-dimensional unit ball B2 under a certain condition, and (4) $\tilde M$ is analytically equivalent to the two-dimensional polydisc ?2 if and only if the homotopic monodoromy group of (M, ?, R) is finite.
15.
Zeta functions and normalized multiple sine functions - Koyama, Shin-ya; Kurokawa, Nobushige
By using normalized multiple sine functions we show expressions for special values of zeta functions and L-functions containing ?(3), ?(5), etc. Our result reveals the importance of division values of normalized multiple sine functions. Properties of multiple Hurwitz zeta functions are crucial for the proof.
1.
