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Journal of the Korean Mathematical Society
Journal Basic Information
pISSN :
0304-9914
eISSN :
2234-3008
Journal DOI :
10.4134/JKMS
Frequency :
Others
Publisher:
The Korean Mathematical Society
Editor in Chief :
Yun Sung Choi
Volume & Issues
Volume 40, Issue 6 - Nov 2003
Volume 40, Issue 5 - Sep 2003
Volume 40, Issue 4 - Jul 2003
Volume 40, Issue 3 - May 2003
Volume 40, Issue 2 - Mar 2003
Volume 40, Issue 1 - Jan 2003
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1
COMPLEX ANALYSIS AND THE FUNK TRANSFORM
Bailey, T.N. ; Eastwood, M.G. ; Gover, A.R. ; Mason, L.J. ;
Journal of the Korean Mathematical Society, volume 40, issue 4, 2003, Pages 577~593
DOI : 10.4134/JKMS.2003.40.4.577
Abstract
The Funk transform is defined by integrating a function on the two-sphere over its great circles. We use complex analysis to invert this transform.
2
SOME EXAMPLES OF HYPERBOLIC HYPERSURFACES IN THE COMPLEX PROJECTIVE SPACE
Fujimoto, Hirotaka ;
Journal of the Korean Mathematical Society, volume 40, issue 4, 2003, Pages 595~607
DOI : 10.4134/JKMS.2003.40.4.595
Abstract
In the previous paper [6], the author constructed hyperbolic hypersurfaces of degree
in the n-dimensional complex projective space for every
. The purpose of this paper is to give some improvement of this result and to show some general methods of constructions of hyperbolic hypersurfaces of higher degree, which enable us to construct hyperbolic hypersurfaces of degree d in the n-dimensional complex projective space for every
.
3
THE EINSTEIN-KÄHLER METRICS ON HUA DOMAIN
Wang, An ; Yin, Weiping ;
Journal of the Korean Mathematical Society, volume 40, issue 4, 2003, Pages 609~627
DOI : 10.4134/JKMS.2003.40.4.609
Abstract
In this paper we describe the Einstein-Kahler metric for the Cartan-Hartogs of the first type which is the special case of the Hua domains. Firstly, we reduce the Monge-Ampere equation for the metric to an ordinary differential equation in the auxiliary function X = X(z, w) = $
w
^2[det(I-ZZ^{T}]^{\frac{1}{K}}$ (see below). This differential equation can be solved to give an implicit function in Χ. Secondly, we get the estimate of the holomorphic section curvature under the complete Einstein-K
hler metric on this domain.
4
EXTENSION OF CR-FUNCTIONS DEFINED ON WEDGE-LIKE DOMAINS IN CR-MANIFOLDS
Zaitsev, Dmitri ; Zampieri, Giuseppe ;
Journal of the Korean Mathematical Society, volume 40, issue 4, 2003, Pages 629~639
DOI : 10.4134/JKMS.2003.40.4.629
Abstract
We give results describing behavior of regions of holomorphic extension of CR functions near boundary points of their domain of definition.
5
THE FORMULA FOR THE SINGULARITY OF SZEGO KERNEL : I
Kuranishi, Masatake ;
Journal of the Korean Mathematical Society, volume 40, issue 4, 2003, Pages 641~666
DOI : 10.4134/JKMS.2003.40.4.641
Abstract
We develop a method of calculating explicitly the singularity of Szego and Bergman kernel by using the process developed by Boutet de Monvel and Sjostrand.
6
HOMOGENEOUS POLYNOMIAL HYPERSURFACE ISOLATED SINGULARITIES
Akahori, Takao ;
Journal of the Korean Mathematical Society, volume 40, issue 4, 2003, Pages 667~680
DOI : 10.4134/JKMS.2003.40.4.667
Abstract
The mirror conjecture means originally the deep relation between complex and symplectic geometry in Calabi-Yau manifolds. Recently, this conjecture is posed beyond Calabi-Yau, and even to, open manifolds (e.g.
singularities and its resolution) is discussed. While if we treat open manifolds, we can't avoid the boundary (in our case, CR manifolds). Therefore we pose the more precise conjecture (mirror symmetry with boundaries). Namely, in mirror symmetry, for boundaries, what kind of structure should correspond\ulcorner For this problem, the
case is studied.
7
THE CONDITIONS FOR REPELLING THE AUTOMORPHISM ORBIT FROM THE BOUNDARY POINT
Byun, Ji-Soo ;
Journal of the Korean Mathematical Society, volume 40, issue 4, 2003, Pages 681~693
DOI : 10.4134/JKMS.2003.40.4.681
Abstract
In this paper, we first prove that there are no automorphism orbits accumulating at a boundary point of the largest isolated finite type. We also present a generalization of the results of Isaev and Krantz on the structure of the orbit accumulation points.
8
SOLVABILITY OF OVERDETERMINED PDE SYSTEMS THAT ADMIT A COMPLETE PROLONGATION AND SOME LOCAL PROBLEMS IN CR GEOMETRY
Han, Chong-Kyu ;
Journal of the Korean Mathematical Society, volume 40, issue 4, 2003, Pages 695~708
DOI : 10.4134/JKMS.2003.40.4.695
Abstract
We study the existence of solutions for overdetermined PDE systems that admit prolongation to a complete system. We reduce the problem to a Pfaffian system on a submanifold of the jet space of unknown functions and then express the integrability conditions in terms of the coefficients of the original system. As possible applications we present some local problems in CR geometry: determining the CR embeddibility into spheres and the existence of infinitesimal CR automorphisms.
9
ANALYTIC APPROACH TO DEFORMATION OF RESOLUTION OF NORMAL ISOLATED SINGULARITIES: FORMAL DEFORMATIONS
Miyajima, Kimio ;
Journal of the Korean Mathematical Society, volume 40, issue 4, 2003, Pages 709~725
DOI : 10.4134/JKMS.2003.40.4.709
Abstract
We give an analytic approach to the versal deformation of a resolution of a germ of normal isolated singularities. In this paper, we treat only formal deformation theory and it is applied to complete the CR-description of the simultaneous resolution of a cone eve. a rational curve of degree n in P
(n
4).
10
STRONGLY PSEUDOCONVEX HANDLEBODIES
Forstneric, Frang ; Kozak, Jernej ;
Journal of the Korean Mathematical Society, volume 40, issue 4, 2003, Pages 727~745
DOI : 10.4134/JKMS.2003.40.4.727
Abstract
We construct strongly pseudoconvex handlebodies in
whose center is a quadratic strongly pseudoconvex domain with an attached flat Lagrangian disc or plane.
11
A VANISHING THEOREM FOR L
^{2}
COHOMOLOGY ON COMPLETE MANIFOLDS
Mcneal, Jeffery-D. ;
Journal of the Korean Mathematical Society, volume 40, issue 4, 2003, Pages 747~756
DOI : 10.4134/JKMS.2003.40.4.747
Abstract
We establish a vanishing theorem on the square-integrable cohomology associated to the Cauchy-Riemann complex on some complete Kaehler manifolds. The hypothesis needed for this result is a growth condition on a primitive of the Kaehler form.