Recent progress in conformal geometry:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Imperial College Press
2007
|
| Series: | ICP advanced texts in mathematics
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 509 S. graph. Darst. |
| ISBN: | 9781860947728 1860947727 |
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MARC
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| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 100 | 1 | |a Bahri, Abbas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Recent progress in conformal geometry |c Abbas Bahri ; Yongzhong Xu |
| 264 | 1 | |a London |b Imperial College Press |c 2007 | |
| 300 | |a XII, 509 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a ICP advanced texts in mathematics |v 1 | |
| 650 | 4 | |a Conformal geometry | |
| 650 | 0 | 7 | |a Konforme Differentialgeometrie |0 (DE-588)4206468-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Globale Differentialgeometrie |0 (DE-588)4021286-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Globale Differentialgeometrie |0 (DE-588)4021286-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Xu, Yongzhong |e Verfasser |4 aut | |
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| 856 | 4 | 2 | |m Digitalisierung UB Augsburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015614645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Record in the Search Index
| _version_ | 1804136469491613696 |
|---|---|
| adam_text | Contents
Preface
v
A. Bahri
and Y.
Хи
1.
Sign-Changing
Yamabe-Type
Problems
1
1.1
General Introduction
...................... 1
1.2
Results and Conditions
..................... 2
1.3
Conjecture
2
and Sketch of the Proof of Theorem
1;
Outline
7
1.4
The Difference of Topology
.................. 11
1.5
Open Problems
......................... 14
1.5.1
Understand the difference of topology
........ 14
1.5.2
Non
critical
asymptots
................. 15
1.5.3
The exit set from infinity
................ 15
1.5.4
Establishing Conjecture
2
and continuous forms of the
discrete inequality
................... 16
1.5.5
The Morse Lemma at infinity, Part I, II, III
..... 16
1.5.6
Notations
ϋ,ϋί,ϊΐί
.................... 16
1.6
Preliminary Estimates and Expansions, the Principal Terms
17
1.7
Preliminary Estimates
..................... 18
1.7.1
The equation satisfied by
v
.............. 19
1.7.2
First estimates on
щ
and hi
.............. 23
1.7.3
The matrix A
...................... 25
1.7.4
Towards an Hp-estimate on
v
і
and an L°°-estimate
on hi
........................... 26
1.7.5
The formal estimate on
/i¡
............... 31
1.7.6
Remarks about the basic estimates
.......... 35
1.7.7
Estimating the right hand side of
Lemma 12..... 35
1.7.8
R,
and the estimate on vi Hi
............. 45
1.8
Proof of the Morse Lemma at Infinity When the
Concentrations are Comparable
................ 54
1.9
Redirecting the Estimates, Estimates on
|i)¿|^i
+
¡h^loo
+
Σ
Фіи
...................
°
....... 66
λ,>λί
1.9.1
Content of Part II
................... 66
1.9.2
Redirecting the estimates
............... 68
1.10
Proof of the Morse Lemma at Infinity
............ 108
1.10.1
Decomposition in groups, gradient and
L°°-estimates on
ϋ,
proof of the Morse Lemma
at infinity
........................ 108
1.10.2
Content of Part HI
................... 108
1.10.3
Basic conformally invariant estimates
......... 109
1.10.4
Estimates on
υ
—
(vi + v¡¡)
.............. 121
1.10.5
The expansion
...................... 129
1.10.6
The coefficient in front of
є^ебе
............ 154
1.10.7
The aj-equation, the estimate on ^
|7¿
I
....... 159
1.10.8
The system of equations corresponding to the
variations of the points
a¿
............... 174
1.10.9
Rule about the variation of the points of
concentrations of the various groups
......... 182
l.lO.lOThe basic parameters and the end of the expansion
. 185
l.lO.HRemarks on the basic parameters
........... 185
1.10.12The end of the expansion and the concluding
remarks
......................... 189
Bibliography
199
Contact Form Geometry
201
2.1
General Introduction
...................... 201
2.2
On the Dynamics of a Contact Structure along a Vector Field
of its Kernel
........................... 205
2.2.1
Introduction
....................... 205
2.2.2
Introducing a large rotation
.............. 210
2.2.3
How
7
is built
...................... 214
2.2.4
Modification of a into aN
............... 226
2.2.5
Computation of
ξΝ
................... 227
235
240
241
275
275
2.2.6
Conformai
deformation
......
2.2.7
Choice of A
............
2.2.8
First step in the construction of A
2.3
Appendix
1...........................
2.3.1
The normal form for
(α, υ)
when a does not turn well
2.4
The Normal Form of (a, v) Near an Attractive Periodic Orbit
of
υ
...............................
2.5
Compactness
..........................
2.5.1
Some basic facts
....................
2.5.2
A model for WB(im), the unstable manifold in
Cß
of
a periodic orbit of index
m
...............
2.5.3
Hypothesis (A), Hypothesis (B), Statement of the
result
...........................
2.5.4
The hole flow
......................
2.5.4.1
Combinatorics
................
2.5.4.2
Normals
....................
2.5.4.3
Hole flow and Normal (Il)-flow on curves of
Y
¿ík
near x°°
..................
2.5.4.4
Forced repetition
...............
2.5.4.5
The Global picture, the degree is zero
. , , .
2.5.5
Companions
.......................
2.5.5.1
Their definition, births and deaths
..... 304
2.5.5.2
Families and nodes nnr
Flow-lines for
Х2ІС+1
to xifj.
The ^-classifying map
2.5.6
2.5.7
2.5.8
276
279
280
282
288
291
291
294
296
299
301
304
305
323
332
The ^classyg p
Small and high oscillation, consecutive characteristic
pieces
334
2.5.9
Iterates of critical points at infinity
.......... 354
2.5.10
The
Fredholm
aspect
.................. 359
2.5.11
Transversality and the compactness argument
....
Transmutations
.........................
2.6.1
Study of the
Poincaré-return
maps
..........
2.6.2
Definition of a basis of
ТаооГ2ѕ
for the reduction of
2.6
2.6.3
Compatibility
......................
2.7
On the Morse Index of a Functional Arising in Contact Form
Geometry
............................
2.7.1
Introduction
......................
2.7.2
The Case of
Г2
.....................
364
384
402
413
417
420
420
424
2.7.3
Darboux Coordinates
.................. 425
2.7.4
The v-transport maps
................. 430
2.7.5
The equations of the characteristic manifold near x°°;
the equations of a critical point
............ 434
2.7.5.1
The characteristic manifold for the unper¬
turbed problem
................ 434
2.7.6
Critical points, vanishing of the determinant
..... 436
2.7.7
Introducing the perturbation
............. 437
2.7.8
The characteristic manifold for the perturbed
problem; the determinant equations
.......... 441
2.7.9
Reduction to the Case fc
= 1.............. 447
2.7.10
Modification of
d2j^(šoo)
|spon{U2,.-,Ufc_,}
...... 454
2.7.11
Calculation of
92Јоо(гоо).и2.из
............ 459
2.8
Calculation of
92Joo(xoo).í¿2.U2
................ 465
2.9
Calculation of i92Jco(500).M2.U4
................ 471
2.10
Other Second Order Derivatives
................ 474
2.11
Appendix
............................ 476
2.11.1
The Proof of Lemma
42................ 476
2.11.2
The proof of Lemma
47 ................ 480
2.11.3
Proof of the Lemmas in
2.7.11............. 483
2.11.4
Proof of Lemma
48................... 483
2.11.5
The Proof of Lemma
49................ 484
2.11.6
The proof of Lemma
50 ................ 485
2.11.7
Proof of Claim
1 .................... 487
2.11.8
Proof of Claim
3 .................... 489
2.11.9
The Final Details of the Calculation of
d2J(x0O).u2.u3
.................... 492
2.11.
lODetails involved in
2.8................. 494
2.11.11Proofof Lemma
52................... 494
2.11.12Proof of Lemma
53................... 495
2.11.13Proof of Claim
3 .................... 496
2.11.14Proofof Claim
4 .................... 497
2.11.
15Details of the Calculation of
Ö2J.M2.U2
........ 503
Bibliography
509
|
| adam_txt |
Contents
Preface
v
A. Bahri
and Y.
Хи
1.
Sign-Changing
Yamabe-Type
Problems
1
1.1
General Introduction
. 1
1.2
Results and Conditions
. 2
1.3
Conjecture
2
and Sketch of the Proof of Theorem
1;
Outline
7
1.4
The Difference of Topology
. 11
1.5
Open Problems
. 14
1.5.1
Understand the difference of topology
. 14
1.5.2
Non
critical
asymptots
. 15
1.5.3
The exit set from infinity
. 15
1.5.4
Establishing Conjecture
2
and continuous forms of the
discrete inequality
. 16
1.5.5
The Morse Lemma at infinity, Part I, II, III
. 16
1.5.6
Notations
ϋ,ϋί,ϊΐί
. 16
1.6
Preliminary Estimates and Expansions, the Principal Terms
17
1.7
Preliminary Estimates
. 18
1.7.1
The equation satisfied by
v
. 19
1.7.2
First estimates on
щ
and hi
. 23
1.7.3
The matrix A
. 25
1.7.4
Towards an Hp-estimate on
v
і
and an L°°-estimate
on hi
. 26
1.7.5
The formal estimate on
/i¡
. 31
1.7.6
Remarks about the basic estimates
. 35
1.7.7
Estimating the right hand side of
Lemma 12. 35
1.7.8
R,
and the estimate on \vi\Hi
. 45
1.8
Proof of the Morse Lemma at Infinity When the
Concentrations are Comparable
. 54
1.9
Redirecting the Estimates, Estimates on
|i)¿|^i
+
¡h^loo
+
Σ
Фіи
.
°
. 66
λ,>λί
1.9.1
Content of Part II
. 66
1.9.2
Redirecting the estimates
. 68
1.10
Proof of the Morse Lemma at Infinity
. 108
1.10.1
Decomposition in groups, gradient and
L°°-estimates on
ϋ,
proof of the Morse Lemma
at infinity
. 108
1.10.2
Content of Part HI
. 108
1.10.3
Basic conformally invariant estimates
. 109
1.10.4
Estimates on
υ
—
(vi + v¡¡)
. 121
1.10.5
The expansion
. 129
1.10.6
The coefficient in front of
є^ебе
. 154
1.10.7
The aj-equation, the estimate on ^
|7¿
I
. 159
1.10.8
The system of equations corresponding to the
variations of the points
a¿
. 174
1.10.9
Rule about the variation of the points of
concentrations of the various groups
. 182
l.lO.lOThe basic parameters and the end of the expansion
. 185
l.lO.HRemarks on the basic parameters
. 185
1.10.12The end of the expansion and the concluding
remarks
. 189
Bibliography
199
Contact Form Geometry
201
2.1
General Introduction
. 201
2.2
On the Dynamics of a Contact Structure along a Vector Field
of its Kernel
. 205
2.2.1
Introduction
. 205
2.2.2
Introducing a large rotation
. 210
2.2.3
How
7
is built
. 214
2.2.4
Modification of a into aN
. 226
2.2.5
Computation of
ξΝ
. 227
235
240
241
275
275
2.2.6
Conformai
deformation
.
2.2.7
Choice of A
.
2.2.8
First step in the construction of A
2.3
Appendix
1.
2.3.1
The normal form for
(α, υ)
when a does not turn well
2.4
The Normal Form of (a, v) Near an Attractive Periodic Orbit
of
υ
.
2.5
Compactness
.
2.5.1
Some basic facts
.
2.5.2
A model for WB(im), the unstable manifold in
Cß
of
a periodic orbit of index
m
.
2.5.3
Hypothesis (A), Hypothesis (B), Statement of the
result
.
2.5.4
The hole flow
.
2.5.4.1
Combinatorics
.
2.5.4.2
Normals
.
2.5.4.3
Hole flow and Normal (Il)-flow on curves of
Y
¿ík
near x°°
.
2.5.4.4
Forced repetition
.
2.5.4.5
The Global picture, the degree is zero
. , , .
2.5.5
Companions
.
2.5.5.1
Their definition, births and deaths
. 304
2.5.5.2
Families and nodes nnr
Flow-lines for
Х2ІС+1
to xifj.
The ^-classifying map
2.5.6
2.5.7
2.5.8
276
279
280
282
288
291
291
294
296
299
301
304
305
323
332
The ^classyg p
Small and high oscillation, consecutive characteristic
pieces
334
2.5.9
Iterates of critical points at infinity
. 354
2.5.10
The
Fredholm
aspect
. 359
2.5.11
Transversality and the compactness argument
.
Transmutations
.
2.6.1
Study of the
Poincaré-return
maps
.
2.6.2
Definition of a basis of
ТаооГ2ѕ
for the reduction of
2.6
2.6.3
Compatibility
.
2.7
On the Morse Index of a Functional Arising in Contact Form
Geometry
.
2.7.1
Introduction
.
2.7.2
The Case of
Г2
.
364
384
402
413
417
420
420
424
2.7.3
Darboux Coordinates
. 425
2.7.4
The v-transport maps
. 430
2.7.5
The equations of the characteristic manifold near x°°;
the equations of a critical point
. 434
2.7.5.1
The characteristic manifold for the unper¬
turbed problem
. 434
2.7.6
Critical points, vanishing of the determinant
. 436
2.7.7
Introducing the perturbation
. 437
2.7.8
The characteristic manifold for the perturbed
problem; the determinant equations
. 441
2.7.9
Reduction to the Case fc
= 1. 447
2.7.10
Modification of
d2j^(šoo)
|spon{U2,.-,Ufc_,}
. 454
2.7.11
Calculation of
92Јоо(гоо).и2.из
. 459
2.8
Calculation of
92Joo(xoo).í¿2.U2
. 465
2.9
Calculation of i92Jco(500).M2.U4
. 471
2.10
Other Second Order Derivatives
. 474
2.11
Appendix
. 476
2.11.1
The Proof of Lemma
42. 476
2.11.2
The proof of Lemma
47 . 480
2.11.3
Proof of the Lemmas in
2.7.11. 483
2.11.4
Proof of Lemma
48. 483
2.11.5
The Proof of Lemma
49. 484
2.11.6
The proof of Lemma
50 . 485
2.11.7
Proof of Claim
1 . 487
2.11.8
Proof of Claim
3 . 489
2.11.9
The Final Details of the Calculation of
d2J(x0O).u2.u3
. 492
2.11.
lODetails involved in
2.8. 494
2.11.11Proofof Lemma
52. 494
2.11.12Proof of Lemma
53. 495
2.11.13Proof of Claim
3 . 496
2.11.14Proofof Claim
4 . 497
2.11.
15Details of the Calculation of
Ö2J.M2.U2
. 503
Bibliography
509 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Bahri, Abbas Xu, Yongzhong |
| author_facet | Bahri, Abbas Xu, Yongzhong |
| author_role | aut aut |
| author_sort | Bahri, Abbas |
| author_variant | a b ab y x yx |
| building | Verbundindex |
| bvnumber | BV022406084 |
| callnumber-first | Q - Science |
| callnumber-label | QA609 |
| callnumber-raw | QA609 |
| callnumber-search | QA609 |
| callnumber-sort | QA 3609 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)144224887 (DE-599)BVBBV022406084 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV022406084 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:20:08Z |
| indexdate | 2024-07-09T20:56:54Z |
| institution | BVB |
| isbn | 9781860947728 1860947727 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015614645 |
| oclc_num | 144224887 |
| open_access_boolean | |
| owner | DE-384 DE-19 DE-BY-UBM DE-824 DE-355 DE-BY-UBR |
| owner_facet | DE-384 DE-19 DE-BY-UBM DE-824 DE-355 DE-BY-UBR |
| physical | XII, 509 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Imperial College Press |
| record_format | marc |
| series | ICP advanced texts in mathematics |
| series2 | ICP advanced texts in mathematics |
| spelling | Bahri, Abbas Verfasser aut Recent progress in conformal geometry Abbas Bahri ; Yongzhong Xu London Imperial College Press 2007 XII, 509 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier ICP advanced texts in mathematics 1 Conformal geometry Konforme Differentialgeometrie (DE-588)4206468-5 gnd rswk-swf Globale Differentialgeometrie (DE-588)4021286-5 gnd rswk-swf Konforme Differentialgeometrie (DE-588)4206468-5 s Globale Differentialgeometrie (DE-588)4021286-5 s DE-604 Xu, Yongzhong Verfasser aut ICP advanced texts in mathematics 1 (DE-604)BV023102173 1 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015614645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bahri, Abbas Xu, Yongzhong Recent progress in conformal geometry ICP advanced texts in mathematics Conformal geometry Konforme Differentialgeometrie (DE-588)4206468-5 gnd Globale Differentialgeometrie (DE-588)4021286-5 gnd |
| subject_GND | (DE-588)4206468-5 (DE-588)4021286-5 |
| title | Recent progress in conformal geometry |
| title_auth | Recent progress in conformal geometry |
| title_exact_search | Recent progress in conformal geometry |
| title_exact_search_txtP | Recent progress in conformal geometry |
| title_full | Recent progress in conformal geometry Abbas Bahri ; Yongzhong Xu |
| title_fullStr | Recent progress in conformal geometry Abbas Bahri ; Yongzhong Xu |
| title_full_unstemmed | Recent progress in conformal geometry Abbas Bahri ; Yongzhong Xu |
| title_short | Recent progress in conformal geometry |
| title_sort | recent progress in conformal geometry |
| topic | Conformal geometry Konforme Differentialgeometrie (DE-588)4206468-5 gnd Globale Differentialgeometrie (DE-588)4021286-5 gnd |
| topic_facet | Conformal geometry Konforme Differentialgeometrie Globale Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015614645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023102173 |
| work_keys_str_mv | AT bahriabbas recentprogressinconformalgeometry AT xuyongzhong recentprogressinconformalgeometry |