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51. CMB 2003 (vol 46 pp. 291)

Sankaran, Parameswaran
A Coincidence Theorem for Holomorphic Maps to $G/P$
The purpose of this note is to extend to an arbitrary generalized Hopf and Calabi-Eckmann manifold the following result of Kalyan Mukherjea: Let $V_n = \mathbb{S}^{2n+1} \times \mathbb{S}^{2n+1}$ denote a Calabi-Eckmann manifold. If $f,g \colon V_n \longrightarrow \mathbb{P}^n$ are any two holomorphic maps, at least one of them being non-constant, then there exists a coincidence: $f(x)=g(x)$ for some $x\in V_n$. Our proof involves a coincidence theorem for holomorphic maps to complex projective varieties of the form $G/P$ where $G$ is complex simple algebraic group and $P\subset G$ is a maximal parabolic subgroup, where one of the maps is dominant.

Categories:32H02, 54M20

52. CMB 2003 (vol 46 pp. 113)

Lee, Jaesung; Rim, Kyung Soo
Properties of the $\mathcal{M}$-Harmonic Conjugate Operator
We define the $\mathcal{M}$-harmonic conjugate operator $K$ and prove that it is bounded on the nonisotropic Lipschitz space and on $\BMO$. Then we show $K$ maps Dini functions into the space of continuous functions on the unit sphere. We also prove the boundedness and compactness properties of $\mathcal{M}$-harmonic conjugate operator with $L^p$ symbol.

Keywords:$\mathcal{M}$-harmonic conjugate operator
Categories:32A70, 47G10

53. CMB 2002 (vol 45 pp. 417)

Kamiyama, Yasuhiko; Tsukuda, Shuichi

Keywords:polygon space, complex structure
Categories:14D20, 32C35

54. CMB 2002 (vol 45 pp. 80)


Keywords:tangential approximation, Carleman
Categories:32E30, 32E25

55. CMB 2001 (vol 44 pp. 150)

Jakóbczak, Piotr

Categories:32A37, 32A22

56. CMB 2001 (vol 44 pp. 105)

Pilipović, Stevan

Categories:32A40, 46F15, 58G07

57. CMB 2001 (vol 44 pp. 126)

Zeron, E. Santillan
Each Copy of the Real Line in $\C^2$ is Removable
Around 1995, Professors Lupacciolu, Chirka and Stout showed that a closed subset of $\C^N$ ($N\geq 2$) is removable for holomorphic functions, if its topological dimension is less than or equal to $N-2$. Besides, they asked whether closed subsets of $\C^2$ homeomorphic to the real line (the simplest 1-dimensional sets) are removable for holomorphic functions. In this paper we propose a positive answer to that question.

Keywords:holomorphic function, removable set

58. CMB 2000 (vol 43 pp. 294)

Bracci, Filippo
Fixed Points of Commuting Holomorphic Maps Without Boundary Regularity
We identify a class of domains of $\C^n$ in which any two commuting holomorphic self-maps have a common fixed point.

Keywords:Holomorphic self-maps, commuting functions, fixed points, Wolff point, Julia's Lemma
Categories:32A10, 32A40, 32H15, 32A30

59. CMB 2000 (vol 43 pp. 174)

Gantz, Christian; Steer, Brian
Stable Parabolic Bundles over Elliptic Surfaces and over Riemann Surfaces

Categories:14J27, 32L07, 14H60, 14D20

60. CMB 2000 (vol 43 pp. 47)

Božičević, Mladen
A Property of Lie Group Orbits

Categories:32B20, 22E15

61. CMB 1999 (vol 42 pp. 499)

Zaharia, Alexandru
Characterizations of Simple Isolated Line Singularities
A line singularity is a function germ $f\colon(\CC ^{n+1},0) \lra\CC$ with a smooth $1$-dimensional critical set $\Sigma=\{(x,y)\in \CC\times \CC^n \mid y=0\}$. An isolated line singularity is defined by the condition that for every $x \neq 0$, the germ of $f$ at $(x,0)$ is equivalent to $y_1^2 +\cdots+y_n ^2$. Simple isolated line singularities were classified by Dirk Siersma and are analogous of the famous $A-D-E$ singularities. We give two new characterizations of simple isolated line singularities.

Categories:32S25, 14B05

62. CMB 1999 (vol 42 pp. 97)

Kwon, E. G.
On Analytic Functions of Bergman $\BMO$ in the Ball

Keywords:Bergman distance, \BMOA$, Hardy space, Bloch function

63. CMB 1998 (vol 41 pp. 129)

Lee, Young Joo
Pluriharmonic symbols of commuting Toeplitz type operators on the weighted Bergman spaces

Keywords:Pluriharmonic functions, Weighted Bergman spaces, Toeplitz type operators.
Categories:47B38, 32A37

64. CMB 1997 (vol 40 pp. 356)

Mazet, Pierre
Principe du maximum et lemme de Schwarz, a valeurs vectorielles

Categories:30C80, 32A30, 46G20, 52A07

65. CMB 1997 (vol 40 pp. 129)

Badea, Catalin
Sur les caractÃ¨res d'une algÃ¨bre de Banach

Categories:46H05, 32A15

66. CMB 1997 (vol 40 pp. 117)

Vigué, Jean-Pierre
Un lemme de Schwarz pour les boules-unitÃ©s ouvertes
Let $B_1$ and $B_2$ be the open unit balls of ${\bbd C}^{n_1}$ and ${\bbd C}^{n_2}$ for the norms $\Vert\,{.}\,\Vert_1$ and $\Vert\,{.}\, \Vert_2$. Let $f \colon B_1 \rightarrow B_2$ be a holomorphic mapping such that $f(0)=0$. It is well known that, for every $z \in B_1$, $\Vert f(z)\Vert_2 \leq \Vert z \Vert_1$, and $\Vert f'(0)\Vert \leq 1$. In this paper, I prove the converse of this result. Let $f \colon B_1 \rightarrow B_2$ be a holomorphic mapping such that $f'(0)$ is an isometry. If $B_2$ is strictly convex, I prove that $f(0) =0$ and that $f$ is linear. I also define the rank of a point $x$ belonging to the boundary of $B_1$ or $B_2$. Under some hypotheses on the ranks, I prove that a holomorphic mapping such that $f(0) = 0$ and that $f'(0)$ is an isometry is linear.

Categories:32H15, 32H02
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