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Structure of a neighbourhood of a complex compact submanifold in a complex manifold

100%
Dwilewicz R.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction...................................................................................................................................................................5 1. Notation and some definitions...................................................................................................................................6   (a) Analytic families.....................................................................................................................................................6   (b) Coordinate neighbourhoods and the normal bundle of a submanifold..................................................................7   (c) A characteristic system for an analytic family.........................................................................................................9   (d) Mutual positions of submanifolds.........................................................................................................................10 2. Sufficient conditions for triviality of the normal bundle.............................................................................................11   (a) Formulations of the conditions.............................................................................................................................11   (b) Connection of condition $(**)_{[U_i]}$ with the normal bundle.............................................................................12   (c) Construction and some properties of functions $f_i$...........................................................................................14   (d) Proof of triviality of the normal bundle.................................................................................................................16   (e) Formulation of the results of Section 2................................................................................................................19 3. A maximum principle for 0-cochains of holomorphic functions on a connected compact complex manifold.............20 4. Construction of an analytic family............................................................................................................................21   (a) Formulation of the main theorem.........................................................................................................................21   (b) Construction of first coefficients of formal power series.......................................................................................23   (c) Some lemmas......................................................................................................................................................25   (d) The induction step - construction of the coefficients $φ_{i|ν+1}$........................................................................28   (e) Proof of the convergence of the formal power series..........................................................................................31   (0 Proof of the main theorem....................................................................................................................................33 Appendix....... .............................................................................................................................................................36   (a) Formulation of sufficient conditions for the convergence of formal power series.................................................36   (b) Some estimates...................................................................................................................................................38   (c) Proof of Proposition A.1.......................................................................................................................................42 References.................................................................................................................................................................44
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Some aspects of holomorphic approximations from the point of view of PDEs

61%
Dwilewicz R., Gauthier P. M.
Banach Center Publications
|
1987
|
tom 19
|
nr 1
79-88
3
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Holomorphic approximation of CR functions on tubular submanifolds of ℂ²

61%
Boivin A., Dwilewicz R.
Annales Polonici Mathematici
|
1991
|
tom 55
|
nr 1
11-18
EN
The purpose of this paper is to take a closer look at uniform semi-global (i.e. on compact subsets) holomorphic approximation of CR functions on tubular submanifolds in ℂ².
4
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Foreword, Contents, List of participants, Lectures and short communications

42%
Dwilewicz R.
Annales Polonici Mathematici
|
1998
|
tom 70
|
nr 1
i-ix
5
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Preface, Contents, List of lectures, List of participants

37%
Bojarski B., Dwilewicz R.
Banach Center Publications
|
1987
|
tom 19
|
nr 1
1-15
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