All issues
Volume 30 (2007)
- Issue 3 Pages 297-
- Issue 2 Pages 157-
- Issue 1 Pages 1-
Predecessor
Volume 30, Issue 2
Displaying 1-9 of 9 articles from this issue
- |<
- <
- 1
- >
- >|
-
Masahiko Yoshinaga2007 Volume 30 Issue 2 Pages 157-194
Published: 2007
Released on J-STAGE: July 04, 2007
JOURNAL FREE ACCESSThe Lefschetz hyperplane section theorem asserts that a complex affine variety is homotopy equivalent to a space obtained from its generic hyperplane section by attaching some cells. The purpose of this paper is to give an explicit description of attaching maps of these cells for the complement of a complex hyperplane arrangement defined over real numbers. The cells and attaching maps are described in combinatorial terms of chambers. We also discuss the cellular chain complex with coefficients in a local system and a presentation for the fundamental group associated to the minimal CW-decomposition for the complement.View full abstractDownload PDF (726K) -
Nobushige Kurokawa, Hiroyuki Ochiai2007 Volume 30 Issue 2 Pages 195-212
Published: 2007
Released on J-STAGE: July 04, 2007
JOURNAL FREE ACCESSDownload PDF (124K) -
Manabu Shirosaki2007 Volume 30 Issue 2 Pages 213-222
Published: 2007
Released on J-STAGE: July 04, 2007
JOURNAL FREE ACCESSWe give a necessary and sufficient condition for a collection of two-point sets to have the uniqueness property for meromorphic functions.View full abstractDownload PDF (111K) -
Mitsuru Nakai2007 Volume 30 Issue 2 Pages 223-236
Published: 2007
Released on J-STAGE: July 04, 2007
JOURNAL FREE ACCESSTake a pair of two disjoint nonpolar compact subsets A and B of the complex plane C = $¥widehat{¥bf C}¥setminus${∞}, the complex sphere less the point at infinity, with connected complement $¥widehat{¥bf C}¥setminus$(A ∪ B) and a simple arc γ in $¥widehat{¥bf C}¥setminus$(A ∪ B). We form the two sheeted covering surface $¥widehat{¥bf C}$γ of $¥widehat{¥bf C}$ by pasting $¥widehat{¥bf C}¥setminus$γ with another copy $¥widehat{¥bf C}¥setminus$γ crosswise along γ. Embed A and B in $¥widehat{¥bf C}$γ either in the same sheet or in the different sheets and consider the variational 2-capacity cap(A, $¥widehat{¥bf C}$γ$¥setminus$B) of A contained in the open subset $¥widehat{¥bf C}$γ$¥setminus$B of $¥widehat{¥bf C}$γ. Concerning the relation between the above capacity and the variational 2-capacity cap(A, $¥widehat{¥bf C}¥setminus$B) of A contained in the open subset $¥widehat{¥bf C}¥setminus$B of $¥widehat{¥bf C}$, we will establish the following capacity inequality for the two sheeted cover and its base:
0 < cap(A, ¥widehat{¥bf C}$γ$¥setminus$B) < 2 · cap(A, ¥widehat{¥bf C}¥setminus$B),
where the bound 2 in the above inequality is the best possible in the sense that, for any 0<τ <2, there is a triple of A, B, and γ such that cap(A, $¥widehat{¥bf C}$γ$¥setminus$B) > τ · cap(A, $¥widehat{¥bf C}¥setminus$B), where A and B may in the same sheet or in the different sheets.View full abstractDownload PDF (133K) -
Georgi Ganchev, Vesselka Mihova2007 Volume 30 Issue 2 Pages 237-245
Published: 2007
Released on J-STAGE: July 04, 2007
JOURNAL FREE ACCESSWe prove that any Kähler manifold admitting a flat complex conformal connection is a Bochner-Kähler manifold with special scalar distribution and zero geometric constants. Applying the local structural theorem for such manifolds we obtain a complete description of the Kähler manifolds under consideration.View full abstractDownload PDF (90K) -
Huiqun Xu2007 Volume 30 Issue 2 Pages 246-251
Published: 2007
Released on J-STAGE: July 04, 2007
JOURNAL FREE ACCESSLet Mn (n ≥ 2) be a n-dimensional oriented closed submanifolds with parallel mean curvature in Sn + p (1), denote by S, the norm square of the second fundamental form of M. H is the constant mean curvature of M. We prove that if ∫M Sn/2 ≤ A (n), where A (n) is a positive universal constant, then M must be a totally umbilical hypersurface in the sphere Sn + 1.View full abstractDownload PDF (75K) -
Jian-Lin Li2007 Volume 30 Issue 2 Pages 252-262
Published: 2007
Released on J-STAGE: July 04, 2007
JOURNAL FREE ACCESSLet Ω and Π be two simply connected domains in the complex plane C, which are not equal to the whole plane C, and let A (Ω, Π) denote the set of functions f : Ω → Π analytic in Ω. Define the quantities Cn (Ω, Π) by
Cn (Ω, Π) := $¥sup¥limits_{f¥in A(¥Omega,¥Pi)}¥sup¥limits_{z¥in ¥Omega} ¥frac{|f^{(n)}(z)|¥lambda_{¥Pi}(f(z))}{n!(¥lambda_{¥Omega}(z))^{n}}$, n ∈ N
where λΩ and λΠ are the densities of the Poincaré metric in Ω and Π, respectively. We derive sharp upper bounds for |f(n)(z)| (z ∈ Ω) and Cn(Ω,Π) if 2 ≤ n ≤ 8 and Ω is a convex domain. The detailed equality condition of the estimate on |f(n)(z)| is also given.View full abstractDownload PDF (105K) -
Janne Heittokangas2007 Volume 30 Issue 2 Pages 263-279
Published: 2007
Released on J-STAGE: July 04, 2007
JOURNAL FREE ACCESSWe 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.View full abstractDownload PDF (136K) -
Naoyuki Koike2007 Volume 30 Issue 2 Pages 280-296
Published: 2007
Released on J-STAGE: July 04, 2007
JOURNAL FREE ACCESSIn this paper, we prove a Chevalley type restriction theorem for a proper complex equifocal submanifold. The proof is performed by showing the same type restriction theorem for an infinite dimensional proper anti-Kaehlerian isoparametric submanifold and using it.View full abstractDownload PDF (181K)
- |<
- <
- 1
- >
- >|