Optimal transport: old and new
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
[2009]
|
| Series: | Grundlehren der mathematischen Wissenschaften
338 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 915 - 956 |
| Physical Description: | xxii, 973 Seiten Illustrationen, Diagramme 235 mm x 155 mm |
| ISBN: | 9783540710493 9783662501801 |
Staff View
MARC
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| 100 | 1 | |a Villani, Cédric |d 1973- |0 (DE-588)13389701X |4 aut | |
| 245 | 1 | 0 | |a Optimal transport |b old and new |c Cédric Villani |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a xxii, 973 Seiten |b Illustrationen, Diagramme |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 338 | |
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Record in the Search Index
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| adam_text |
Contents
Preface
.
VII
Conventions.
XVII
Introduction
1
1
Couplings and changes of variables
. 5
2
Three examples of coupling techniques
. 21
3
The founding fathers of optimal transport
. 29
Part I Qualitative description of optimal transport
39
4
Basic properties
. 43
5
Cyclical
monotonicity
and Kantorovich duality
. 51
6
The
Wasserstein
distances
. 93
7
Displacement interpolation
.113
8
The Monge-Mather shortening principle
.163
9
Solution of the
Monge
problem I: Global approach
. 205
10
Solution of the
Monge
problem II: Local approach
. 215
XIII
XIV Contents
11
The Jacobian equation
.273
12
Smoothness
.281
13
Qualitative picture
.333
Part II Optimal transport and Riemannian geometry
353
14
Ricci
curvature
.357
15
Otto calculus
.421
16
Displacement convexity I
.435
17
Displacement convexity II
.449
18
Volume control
.493
19
Density control and local regularity
.505
20
Infinitesimal displacement convexity
.525
21
Isoperimetric-type inequalities
.545
22
Concentration inequalities
.567
23
Gradient flows 1
.629
24
Gradient flows II: Qualitative properties
.693
25
Gradient flows III: Functional inequalities
.719
Part III Synthetic treatment of
Ricci
curvature
731
26
Analytic and synthetic points of view
.735
27
Convergence of metric-measure spaces
.743
28
Stability of optimal transport
.773
Contents
XV
29
Weak
Ricci
curvature bounds I: Definition
and Stability
.795
30
Weak
Ricci
curvature bounds II: Geometric
and analytic properties
.847
Conclusions and open problems
903
References
.915
List of short statements
.957
List of figures
.965
Index
.967
Some notable cost functions
.971 |
| adam_txt |
Contents
Preface
.
VII
Conventions.
XVII
Introduction
1
1
Couplings and changes of variables
. 5
2
Three examples of coupling techniques
. 21
3
The founding fathers of optimal transport
. 29
Part I Qualitative description of optimal transport
39
4
Basic properties
. 43
5
Cyclical
monotonicity
and Kantorovich duality
. 51
6
The
Wasserstein
distances
. 93
7
Displacement interpolation
.113
8
The Monge-Mather shortening principle
.163
9
Solution of the
Monge
problem I: Global approach
. 205
10
Solution of the
Monge
problem II: Local approach
. 215
XIII
XIV Contents
11
The Jacobian equation
.273
12
Smoothness
.281
13
Qualitative picture
.333
Part II Optimal transport and Riemannian geometry
353
14
Ricci
curvature
.357
15
Otto calculus
.421
16
Displacement convexity I
.435
17
Displacement convexity II
.449
18
Volume control
.493
19
Density control and local regularity
.505
20
Infinitesimal displacement convexity
.525
21
Isoperimetric-type inequalities
.545
22
Concentration inequalities
.567
23
Gradient flows 1
.629
24
Gradient flows II: Qualitative properties
.693
25
Gradient flows III: Functional inequalities
.719
Part III Synthetic treatment of
Ricci
curvature
731
26
Analytic and synthetic points of view
.735
27
Convergence of metric-measure spaces
.743
28
Stability of optimal transport
.773
Contents
XV
29
Weak
Ricci
curvature bounds I: Definition
and Stability
.795
30
Weak
Ricci
curvature bounds II: Geometric
and analytic properties
.847
Conclusions and open problems
903
References
.915
List of short statements
.957
List of figures
.965
Index
.967
Some notable cost functions
.971 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Villani, Cédric 1973- |
| author_GND | (DE-588)13389701X |
| author_facet | Villani, Cédric 1973- |
| author_role | aut |
| author_sort | Villani, Cédric 1973- |
| author_variant | c v cv |
| building | Verbundindex |
| bvnumber | BV035103311 |
| classification_rvk | SI 990 SK 870 SK 880 SK 970 |
| classification_tum | MAT 900f MAT 490f MAT 530f |
| ctrlnum | (OCoLC)262279119 (DE-599)DNB98984577X |
| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:14:58Z |
| indexdate | 2024-09-24T00:16:22Z |
| institution | BVB |
| isbn | 9783540710493 9783662501801 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016771254 |
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| physical | xxii, 973 Seiten Illustrationen, Diagramme 235 mm x 155 mm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | Springer |
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| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Villani, Cédric 1973- (DE-588)13389701X aut Optimal transport old and new Cédric Villani Berlin ; Heidelberg Springer [2009] © 2009 xxii, 973 Seiten Illustrationen, Diagramme 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 338 Literaturverzeichnis: Seite 915 - 956 Reihenfolgeproblem (DE-588)4242167-6 gnd rswk-swf Transportproblem (DE-588)4060694-6 gnd rswk-swf Transportproblem (DE-588)4060694-6 s DE-604 Reihenfolgeproblem (DE-588)4242167-6 s Erscheint auch als Online-Ausgabe 978-3-540-71050-9 Grundlehren der mathematischen Wissenschaften 338 (DE-604)BV000000395 338 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016771254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Villani, Cédric 1973- Optimal transport old and new Grundlehren der mathematischen Wissenschaften Reihenfolgeproblem (DE-588)4242167-6 gnd Transportproblem (DE-588)4060694-6 gnd |
| subject_GND | (DE-588)4242167-6 (DE-588)4060694-6 |
| title | Optimal transport old and new |
| title_auth | Optimal transport old and new |
| title_exact_search | Optimal transport old and new |
| title_exact_search_txtP | Optimal transport old and new |
| title_full | Optimal transport old and new Cédric Villani |
| title_fullStr | Optimal transport old and new Cédric Villani |
| title_full_unstemmed | Optimal transport old and new Cédric Villani |
| title_short | Optimal transport |
| title_sort | optimal transport old and new |
| title_sub | old and new |
| topic | Reihenfolgeproblem (DE-588)4242167-6 gnd Transportproblem (DE-588)4060694-6 gnd |
| topic_facet | Reihenfolgeproblem Transportproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016771254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT villanicedric optimaltransportoldandnew |