CR manifolds and the tangential Cauchy-Riemann complex:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. u.a.
CRC Press
1991
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| Series: | Studies in advanced mathematics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 364 S. graph. Darst. |
| ISBN: | 084937152X |
Staff View
MARC
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| 100 | 1 | |a Boggess, Albert |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a CR manifolds and the tangential Cauchy-Riemann complex |c Albert Boggess |
| 264 | 1 | |a Boca Raton, Fla. u.a. |b CRC Press |c 1991 | |
| 300 | |a XVII, 364 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Studies in advanced mathematics | |
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| 650 | 7 | |a Géométrie différentielle |2 ram | |
| 650 | 4 | |a CR submanifolds | |
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Record in the Search Index
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| adam_text | Contents
Contents vii
Introduction xiii
PART I: PRELIMINARIES 1
1 Analysis on Euclidean Space 2
1.1 Functions 2
1.2 Vectors and vector fields 7
1.3 Forms 9
1.4 The exterior derivative 12
1.5 Contractions 15
2 Analysis on Manifolds 17
2.1 Manifolds 17
2.2 Submanifolds 19
2.3 Vectors on manifolds 23
2.4 Forms on manifolds 26
2.5 Integration on manifolds 29
3 Complexified Vectors and Forms 39
3.1 Complexification of a real vector space 39
vii
viii Contents
3.2 Complex structures 41
3.3 Higher degree complexified forms 45
4 The Frobenius Theorem 51
4.1 The real Frobenius theorem 51
4.2 The analytic Frobenius theorem 56
4.3 Almost complex structures 58
J Distribution Theory 61
5.1 The spaces V and £ 61
5.2 Operations with distributions 65
5.3 Whitney s extension theorem 71
5.4 Fundamental solutions for partial differential equations 74
6 Currents 79
6.1 Definitions 79
6.2 Operations with currents 84
PART II: CR MANIFOLDS 95
7 CR Manifolds 97
7.1 Imbedded CR manifolds 97
7.2 A normal form for a generic CR submanifold 103
7.3 Quadric submanifolds 111
7.4 Abstract CR manifolds 120
8 The Tangential Cauchy Riemann Complex 122
8.1 Extrinsic approach 122
8.2 Intrinsic approach to 8m 130
8.3 The equivalence of the extrinsic and intrinsic tangential
Cauchy Riemann complexes 134
9 CR Functions and Maps 140
9.1 CR functions 140
9.2 CR maps 149
10 The Levi Form 156
10.1 Definitions 156
10.2 The Levi form for an imbedded CR manifold 159
Contents ix
10.3 The Levi form of a real hypersurface 163
11 The Imbeddability ofCR Manifolds 169
11.1 The real analytic imbedding theorem 169
11.2 Nirenberg s nonimbeddable example 172
12 Further Results 179
12.1 Bloom Graham normal form 179
12.2 Rigid and semirigid submanifolds 183
12.3 More on the Levi form 185
12.4 Kuranishi s imbedding theorem 187
12.5 Nongeneric and non CR manifolds 187
PART III: THE HOLOMORPHIC EXTENSION OF CR
FUNCTIONS 189
13 An Approximation Theorem 191
14 The Statement of the CR Extension Theorem 198
14.1 Lewy s CR extension theorem for hypersurfaces 198
14.2 The CR extension theorem for higher codimension 200
14.3 Examples 202
ij The Analytic Disc Technique 206
15.1 Reduction to analytic discs 207
15.2 Analytic discs for hypersurfaces 208
15.3 Analytic discs for quadric submanifolds 210
15.4 Bishop s equation 214
15.5 The proof of the analytic disc theorem for the general case 221
16 The Fourier Transform Technique 229
16.1 A Fourier inversion formula 230
16.2 The hypoanalytic wave front set 237
16.3 The hypoanalytic wave front set and the Levi form 244
17 Further Results 251
17.1 The Fourier integral approach in the nonrigid case 251
17.2 The holomorphic extension of CR distributions 254
17.3 CR extension near points of higher type 257
x Contents
17.4 Analytic hypoellipticity 260
PART IV: SOLVABILITY OF THE TANGENTIAL
CAUCHY RIEMANN COMPLEX 263
18 Kernel Calculus 265
18.1 Definitions 265
18.2 A homotopy formula 272
19 Fundamental Solutions for the Exterior Derivative
and Cauchy Riemann Operators 277
19.1 Fundamental solutions for d on RN 278
19.2 Fundamental solutions for 9onC 281
19.3 Bochner s global CR extension theorem 291
20 The Kernels of Henkin 294
20.1 A general class of kernels 294
20.2 A formal identity 297
20.3 The solution to the Cauchy Riemann equations
on a convex domain 299
20.4 Boundary value results for Henkin s kernels 303
21 Fundamental Solutions for the Tangential
Cauchy Riemann Complex on a Convex
Hypersurface 312
21.1 The first fundamental solution for the tangential
Cauchy Riemann complex 312
21.2 A second fundamental solution to the tangential
Cauchy Riemann complex 317
22 A Local Solution to the Tangential
Cauchy Riemann Equations 327
23 Local Nonsolvability of the Tangential
Cauchy Riemann Complex 334
23.1 Hans Lewy s nonsolvability example 334
23.2 Henkin s criterion for local solvability at the top degree 337
Contents xi
24 Further Results 342
24.1 More on the Bochner Martinelli kernel 342
24.2 Kernels for strictly pseudoconvex boundaries 345
24.3 Further estimates on the solution to 8m 348
24.4 Weakly convex boundaries 348
24.5 Solvability of the tangential Cauchy Riemann complex
in other geometries 349
Bibliography 354
Notation 359
Index 361
|
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| id | DE-604.BV004731103 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:16:50Z |
| institution | BVB |
| isbn | 084937152X |
| language | English |
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| oclc_num | 24217987 |
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| owner | DE-12 DE-739 DE-11 |
| owner_facet | DE-12 DE-739 DE-11 |
| physical | XVII, 364 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Studies in advanced mathematics |
| spelling | Boggess, Albert Verfasser aut CR manifolds and the tangential Cauchy-Riemann complex Albert Boggess Boca Raton, Fla. u.a. CRC Press 1991 XVII, 364 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in advanced mathematics CR-sousvariétés ram Cauchy-Riemann, Équations de ram Géométrie différentielle ram CR submanifolds Cauchy-Riemann equations Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd rswk-swf Cauchy-Riemannscher Komplex (DE-588)4199639-2 gnd rswk-swf Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 s DE-604 Cauchy-Riemannscher Komplex (DE-588)4199639-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002909839&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boggess, Albert CR manifolds and the tangential Cauchy-Riemann complex CR-sousvariétés ram Cauchy-Riemann, Équations de ram Géométrie différentielle ram CR submanifolds Cauchy-Riemann equations Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd Cauchy-Riemannscher Komplex (DE-588)4199639-2 gnd |
| subject_GND | (DE-588)4147400-4 (DE-588)4199639-2 |
| title | CR manifolds and the tangential Cauchy-Riemann complex |
| title_auth | CR manifolds and the tangential Cauchy-Riemann complex |
| title_exact_search | CR manifolds and the tangential Cauchy-Riemann complex |
| title_full | CR manifolds and the tangential Cauchy-Riemann complex Albert Boggess |
| title_fullStr | CR manifolds and the tangential Cauchy-Riemann complex Albert Boggess |
| title_full_unstemmed | CR manifolds and the tangential Cauchy-Riemann complex Albert Boggess |
| title_short | CR manifolds and the tangential Cauchy-Riemann complex |
| title_sort | cr manifolds and the tangential cauchy riemann complex |
| topic | CR-sousvariétés ram Cauchy-Riemann, Équations de ram Géométrie différentielle ram CR submanifolds Cauchy-Riemann equations Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd Cauchy-Riemannscher Komplex (DE-588)4199639-2 gnd |
| topic_facet | CR-sousvariétés Cauchy-Riemann, Équations de Géométrie différentielle CR submanifolds Cauchy-Riemann equations Cauchy-Riemannsche Mannigfaltigkeit Cauchy-Riemannscher Komplex |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002909839&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT boggessalbert crmanifoldsandthetangentialcauchyriemanncomplex |