Prescribing scalar curvature in conformal geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Germany
EMS Press
[2023]
|
| Schriftenreihe: | Zurich lectures in advanced mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | x, 151 Seiten Illustrationen, Diagramme 24 cm |
| ISBN: | 9783985470525 3985470529 |
Internformat
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| 100 | 1 | |a Malchiodi, Andrea |e Verfasser |0 (DE-588)130563021 |4 aut | |
| 245 | 1 | 0 | |a Prescribing scalar curvature in conformal geometry |c Andrea Malchiodi |
| 264 | 1 | |a Berlin, Germany |b EMS Press |c [2023] | |
| 300 | |a x, 151 Seiten |b Illustrationen, Diagramme |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Zurich lectures in advanced mathematics | |
| 650 | 0 | 7 | |a Skalare Krümmung |0 (DE-588)4808160-7 |2 gnd |9 rswk-swf |
| 653 | |a prescribed scalar curvature | ||
| 653 | |a elliptic equations of critical type | ||
| 653 | |a blow-up analysis | ||
| 653 | |a topological methods | ||
| 689 | 0 | 0 | |a Skalare Krümmung |0 (DE-588)4808160-7 |D s |
| 689 | 0 | |5 DE-604 | |
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Datensatz im Suchindex
| _version_ | 1804186457898745856 |
|---|---|
| adam_text | PREFACE
.....................................................................................................................
VII
1
INTRODUCTION
........................................................................................................
1
1.1
PROBLEM
(KW-1)
.......................................................................................
2
1.2
PROBLEM
(KW-2)
.......................................................................................
3
1.3
VARIATIONAL
ANALYSIS
OF
(KW-2)
.................................................................
4
1.4
SUB-CRITICAL
APPROXIMATION
AND
BLOW-UP
ANALYSIS
..................................
6
1.5
SOME
GENERAL
EXISTENCE
RESULTS
.................................................................
8
2
PRELIMINARIES
.....................................................................................................
11
2.1
A
QUICK
REVIEW
OF
DIFFERENTIAL
GEOMETRY
..................................................
11
2.2
CONFORMAL
CHANGES
OF
METRIC
..................................................................
16
2.3
HOLDER
AND
SOBOLEV
SPACES
ON
CLOSED
MANIFOLDS
....................................
17
2.4
REGULARITY
AND
EXISTENCE
THEORY
FOR
LINEAR
ELLIPTIC
OPERATORS
.................
18
2.5
REGULARITY
OF
WEAK
SOLUTIONS
TO
SOME
NON-LINEAR
EQUATIONS
...................
19
3
THE
YAMABE
QUOTIENT
AND
RESOLUTION
OF
(KW-1)
.........................................
23
3.1
ON
THE
FIRST
EIGENVALUE
OF
L
G
AND
THE
YAMABE
QUOTIENT
..........................
23
3.2
SPHERICAL
DECREASING
REARRANGEMENT
......................................................
27
3.3
THE
YAMABE
QUOTIENT
OF
THE
STANDARD
SPHERE
...........................................
31
3.4
EXISTENCE
OF
YAMABE
METRICS
..................................................................
33
3.5
PROOF
OF
THEOREM
A
..................................................................................
38
4
VARIATIONAL
STRUCTURE
OF
(KW-2)
....................................................................
41
4.1
EXISTENCE
AND
UNIQUENESS
FOR
NON-POSITIVE
CURVATURES
..........................
41
4.2
VARIATIONAL
APPROACH
IN
POSITIVE
CURVATURE
............................................
43
4.3
PROOF
OF
THEOREM
B
..................................................................................
47
5
CLASSIFICATION
OF
ENTIRE
SOLUTIONS
IN
THE
EUCLIDEAN
SPACE
...........................
51
5.1
MOVING
PLANES
AND
MOVING
SPHERES
.........................................................
51
5.2
LIOUVILLE
THEOREM
IN
THE
SUB-CRITICAL
CASE
...............................................
56
6
BLOW-UP
ANALYSIS
...............................................................................................
61
6.1
ISOLATED
AND
ISOLATED-SIMPLE
BLOW-UPS
....................................................
62
6.2
BLOW-UP
ANALYSIS
IN
DIMENSIONS
3
AND
4
..................................................
70
7
FINITE-DIMENSIONAL
REDUCTION
OF
(EK,V)
.........................................................
77
7.1
LYAPUNOV-SCHMIDT
REDUCTION
.................................................................
78
7.2
EXISTENCE
OF
BLOWING-UP
SOLUTIONS
TO
(EK,
............................................
83
7.3
BLOW-UP
ANALYSIS
IN
ARBITRARY
DIMENSION
..............................................
86
8
GENERAL
EXISTENCE
RESULTS
FOR
(EX)
.................................................................
91
8.1
PROOF
OF
THEOREM
C
.................................................................................
91
8.2
EXISTENCE
RESULTS
VIA
MIN-MAX
THEORY
..................................................
96
8.3
PROOF
OF
THEOREM
D
....................................................................................
101
9
FORBIDDEN
CURVATURES
.........................................................................................
107
9.1
FIRST
NON-EXISTENCE
RESULTS
.........................................................................
107
9.2
FORBIDDEN
FUNCTIONS
WITH
A
GIVEN
MORSE
STRUCTURE
.................................
109
9.3
BLOW-UP
ANALYSIS
VIA
STUDY
OF
SINGULAR
SOLUTIONS
....................................
113
10
RELATED
DIRECTIONS
AND
PERSPECTIVES
................................................................
119
10.1
BLOW-UP
ANALYSIS
IN
GENERAL
DIMENSIONS
...................................................
119
10.2
MORSE
THEORY
AND
MORSE
HOMOLOGY
..........................................................
120
10.3
HIGHER-ORDER
AND
FULLY
NON-LINEAR
VERSIONS
..............................................
122
10.4
MANIFOLDS
WITH
BOUNDARY
...........................................................................
124
10.5
THE
COMPLETE
CASE
.....................................................................................
126
10.6
THE
EINSTEIN
CONSTRAINT
EQUATIONS
.............................................................
127
A
SOME
USEFUL
RESULTS
.............................................................................................
131
A.
1
POHOZAEV
S
IDENTITY
.....................................................................................
131
A.
2
KAZDAN-WARNER
IDENTITY
...........................................................................
133
A.3
A
RIGIDITY
RESULT
..........................................................................................
135
REFERENCES
...................................................................................................................
139
|
| adam_txt |
PREFACE
.
VII
1
INTRODUCTION
.
1
1.1
PROBLEM
(KW-1)
.
2
1.2
PROBLEM
(KW-2)
.
3
1.3
VARIATIONAL
ANALYSIS
OF
(KW-2)
.
4
1.4
SUB-CRITICAL
APPROXIMATION
AND
BLOW-UP
ANALYSIS
.
6
1.5
SOME
GENERAL
EXISTENCE
RESULTS
.
8
2
PRELIMINARIES
.
11
2.1
A
QUICK
REVIEW
OF
DIFFERENTIAL
GEOMETRY
.
11
2.2
CONFORMAL
CHANGES
OF
METRIC
.
16
2.3
HOLDER
AND
SOBOLEV
SPACES
ON
CLOSED
MANIFOLDS
.
17
2.4
REGULARITY
AND
EXISTENCE
THEORY
FOR
LINEAR
ELLIPTIC
OPERATORS
.
18
2.5
REGULARITY
OF
WEAK
SOLUTIONS
TO
SOME
NON-LINEAR
EQUATIONS
.
19
3
THE
YAMABE
QUOTIENT
AND
RESOLUTION
OF
(KW-1)
.
23
3.1
ON
THE
FIRST
EIGENVALUE
OF
L
G
AND
THE
YAMABE
QUOTIENT
.
23
3.2
SPHERICAL
DECREASING
REARRANGEMENT
.
27
3.3
THE
YAMABE
QUOTIENT
OF
THE
STANDARD
SPHERE
.
31
3.4
EXISTENCE
OF
YAMABE
METRICS
.
33
3.5
PROOF
OF
THEOREM
A
.
38
4
VARIATIONAL
STRUCTURE
OF
(KW-2)
.
41
4.1
EXISTENCE
AND
UNIQUENESS
FOR
NON-POSITIVE
CURVATURES
.
41
4.2
VARIATIONAL
APPROACH
IN
POSITIVE
CURVATURE
.
43
4.3
PROOF
OF
THEOREM
B
.
47
5
CLASSIFICATION
OF
ENTIRE
SOLUTIONS
IN
THE
EUCLIDEAN
SPACE
.
51
5.1
MOVING
PLANES
AND
MOVING
SPHERES
.
51
5.2
LIOUVILLE
THEOREM
IN
THE
SUB-CRITICAL
CASE
.
56
6
BLOW-UP
ANALYSIS
.
61
6.1
ISOLATED
AND
ISOLATED-SIMPLE
BLOW-UPS
.
62
6.2
BLOW-UP
ANALYSIS
IN
DIMENSIONS
3
AND
4
.
70
7
FINITE-DIMENSIONAL
REDUCTION
OF
(EK,V)
.
77
7.1
LYAPUNOV-SCHMIDT
REDUCTION
.
78
7.2
EXISTENCE
OF
BLOWING-UP
SOLUTIONS
TO
(EK,
.
83
7.3
BLOW-UP
ANALYSIS
IN
ARBITRARY
DIMENSION
.
86
8
GENERAL
EXISTENCE
RESULTS
FOR
(EX)
.
91
8.1
PROOF
OF
THEOREM
C
.
91
8.2
EXISTENCE
RESULTS
VIA
MIN-MAX
THEORY
.
96
8.3
PROOF
OF
THEOREM
D
.
101
9
FORBIDDEN
CURVATURES
.
107
9.1
FIRST
NON-EXISTENCE
RESULTS
.
107
9.2
FORBIDDEN
FUNCTIONS
WITH
A
GIVEN
MORSE
STRUCTURE
.
109
9.3
BLOW-UP
ANALYSIS
VIA
STUDY
OF
SINGULAR
SOLUTIONS
.
113
10
RELATED
DIRECTIONS
AND
PERSPECTIVES
.
119
10.1
BLOW-UP
ANALYSIS
IN
GENERAL
DIMENSIONS
.
119
10.2
MORSE
THEORY
AND
MORSE
HOMOLOGY
.
120
10.3
HIGHER-ORDER
AND
FULLY
NON-LINEAR
VERSIONS
.
122
10.4
MANIFOLDS
WITH
BOUNDARY
.
124
10.5
THE
COMPLETE
CASE
.
126
10.6
THE
EINSTEIN
CONSTRAINT
EQUATIONS
.
127
A
SOME
USEFUL
RESULTS
.
131
A.
1
POHOZAEV
'
S
IDENTITY
.
131
A.
2
KAZDAN-WARNER
IDENTITY
.
133
A.3
A
RIGIDITY
RESULT
.
135
REFERENCES
.
139 |
| any_adam_object | 1 |
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| author_GND | (DE-588)130563021 |
| author_facet | Malchiodi, Andrea |
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| dewey-ones | 516 - Geometry |
| dewey-raw | 516.362 |
| dewey-search | 516.362 |
| dewey-sort | 3516.362 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV049588085 |
| illustrated | Illustrated |
| index_date | 2024-07-03T23:32:56Z |
| indexdate | 2024-07-10T10:11:26Z |
| institution | BVB |
| institution_GND | (DE-588)1066118477 |
| isbn | 9783985470525 3985470529 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034932830 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | x, 151 Seiten Illustrationen, Diagramme 24 cm |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | EMS Press |
| record_format | marc |
| series2 | Zurich lectures in advanced mathematics |
| spelling | Malchiodi, Andrea Verfasser (DE-588)130563021 aut Prescribing scalar curvature in conformal geometry Andrea Malchiodi Berlin, Germany EMS Press [2023] x, 151 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Zurich lectures in advanced mathematics Skalare Krümmung (DE-588)4808160-7 gnd rswk-swf prescribed scalar curvature elliptic equations of critical type blow-up analysis topological methods Skalare Krümmung (DE-588)4808160-7 s DE-604 European Mathematical Society Publishing House ETH-Zentrum SEW A27 (DE-588)1066118477 pbl Erscheint auch als Online-Ausgabe 978-3-98547-552-0 B:DE-101 application/pdf https://d-nb.info/1302490575/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034932830&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p dnb 20240119 DE-101 https://d-nb.info/provenance/plan#dnb |
| spellingShingle | Malchiodi, Andrea Prescribing scalar curvature in conformal geometry Skalare Krümmung (DE-588)4808160-7 gnd |
| subject_GND | (DE-588)4808160-7 |
| title | Prescribing scalar curvature in conformal geometry |
| title_auth | Prescribing scalar curvature in conformal geometry |
| title_exact_search | Prescribing scalar curvature in conformal geometry |
| title_exact_search_txtP | Prescribing scalar curvature in conformal geometry |
| title_full | Prescribing scalar curvature in conformal geometry Andrea Malchiodi |
| title_fullStr | Prescribing scalar curvature in conformal geometry Andrea Malchiodi |
| title_full_unstemmed | Prescribing scalar curvature in conformal geometry Andrea Malchiodi |
| title_short | Prescribing scalar curvature in conformal geometry |
| title_sort | prescribing scalar curvature in conformal geometry |
| topic | Skalare Krümmung (DE-588)4808160-7 gnd |
| topic_facet | Skalare Krümmung |
| url | https://d-nb.info/1302490575/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034932830&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT malchiodiandrea prescribingscalarcurvatureinconformalgeometry AT europeanmathematicalsocietypublishinghouseethzentrumsewa27 prescribingscalarcurvatureinconformalgeometry |
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