Mean curvature flow and isoperimetric inequalities:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2010
|
| Series: | Advanced courses in mathematics - CRM Barcelona
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 113 S. |
| ISBN: | 9783034602129 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mean curvature flow and isoperimetric inequalities |c Manuel Ritoré ; Carlo Sinestrari |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2010 | |
| 300 | |a VIII, 113 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Advanced courses in mathematics - CRM Barcelona | |
| 650 | 4 | |a Flows (Differentiable dynamical systems) | |
| 650 | 4 | |a Isoperimetric inequalities | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Foreword
I Formation of Singularities in the Mean Curvature Flow
Carlo Sinestrari
1
1
Introduction
............................... 3
2
Geometry of hypersurfaces
....................... 5
3
Examples
................................ 9
4
Local existence and formation of singularities
............ 10
5
Invariance
properties
.......................... 16
6
Singular behaviour of convex surfaces
................ 20
7
Convexity estimates
.......................... 23
8
Rescaling near a singularity
...................... 25
9
Huisken s monotonicity formula
.................... 28
10
Cylindrical and gradient estimates
.................. 32
11
Mean curvature flow with surgeries
.................. 36
Bibliography
................................. 39
II Geometric Flows, Isoperimetric Inequalities and
Hyperbolic Geometry
Manuel
Rüoré
45
Preface
49
1
The classical isoperimetric inequality
m
Euclidean space
53
1.1
Introduction
............................... 53
1.2
Preliminaries
.............................. 53
1.2.1
Area and volume
........................ 53
1.2.2
Variational formulas
...................... 55
1.2.3
The isoperimetric profile
.................... 56
1.2.4
Isoperimetric regions
...................... 57
viii Contents
1.3
The isoperimetric inequality in Euclidean space
........... 58
1.3.1
A calibration argument
.................... 59
1.3.2 Schwarz symmetrization.................... 61
1.3.3
Another proof of the isoperimetric inequality
........ 66
2
Surfaces
69
2.1
Introduction
............................... 69
2.1.1
The Gauss-Bonnet Theorem
................. 70
2.2
Curve shortening flow
......................... 72
2.2.1
Basic results
.......................... 72
2.2.2
The avoidance principle
.................... 74
2.3
Applications of curve shortening flow to isoperimetric inequalities
. 75
2.3.1
Planes
.............................. 75
2.3.2
Spheres
............................. 82
3
Higher dimensions
85
3.1
Introduction
............................... 85
3.2
Hk-ñows
and isoperimetric inequalities
................ 86
3.3
Estimates on the Willmore functional and isoperimetric inequalities
89
3.3.1
Euclidean spaces
........................ 89
3.3.2
3-dimensional
Hadamard
manifolds
.............. 91
3.4
Singularities in the volume-preserving mean curvature flow
.... 96
4
Some applications to hyperbolic geometry
99
4.1
Introduction
............................... 99
4.2
Bounds on the Heegaard genus of a hyperbolic manifold
...... 100
4.3
The isoperimetric profile for small volumes
.............. 102
Bibliography
105
|
| any_adam_object | 1 |
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| callnumber-label | QA614 |
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| ctrlnum | (OCoLC)436266252 (DE-599)DNB995948380 |
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| dewey-ones | 516 - Geometry |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV036069610 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:10:49Z |
| institution | BVB |
| isbn | 9783034602129 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018960911 |
| oclc_num | 436266252 |
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| owner | DE-355 DE-BY-UBR DE-384 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-11 |
| physical | VIII, 113 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Advanced courses in mathematics - CRM Barcelona |
| spelling | Mean curvature flow and isoperimetric inequalities Manuel Ritoré ; Carlo Sinestrari Basel [u.a.] Birkhäuser 2010 VIII, 113 S. txt rdacontent n rdamedia nc rdacarrier Advanced courses in mathematics - CRM Barcelona Flows (Differentiable dynamical systems) Isoperimetric inequalities Isoperimetrische Ungleichung (DE-588)4162544-4 gnd rswk-swf Fluss Mathematik (DE-588)4489499-5 gnd rswk-swf Fluss Mathematik (DE-588)4489499-5 s Isoperimetrische Ungleichung (DE-588)4162544-4 s DE-604 Ritoré, Manuel Sonstige oth Sinestrari, Carlo Sonstige oth Erscheint auch als Online-Ausgabe 978-3-0346-0213-6 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018960911&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mean curvature flow and isoperimetric inequalities Flows (Differentiable dynamical systems) Isoperimetric inequalities Isoperimetrische Ungleichung (DE-588)4162544-4 gnd Fluss Mathematik (DE-588)4489499-5 gnd |
| subject_GND | (DE-588)4162544-4 (DE-588)4489499-5 |
| title | Mean curvature flow and isoperimetric inequalities |
| title_auth | Mean curvature flow and isoperimetric inequalities |
| title_exact_search | Mean curvature flow and isoperimetric inequalities |
| title_full | Mean curvature flow and isoperimetric inequalities Manuel Ritoré ; Carlo Sinestrari |
| title_fullStr | Mean curvature flow and isoperimetric inequalities Manuel Ritoré ; Carlo Sinestrari |
| title_full_unstemmed | Mean curvature flow and isoperimetric inequalities Manuel Ritoré ; Carlo Sinestrari |
| title_short | Mean curvature flow and isoperimetric inequalities |
| title_sort | mean curvature flow and isoperimetric inequalities |
| topic | Flows (Differentiable dynamical systems) Isoperimetric inequalities Isoperimetrische Ungleichung (DE-588)4162544-4 gnd Fluss Mathematik (DE-588)4489499-5 gnd |
| topic_facet | Flows (Differentiable dynamical systems) Isoperimetric inequalities Isoperimetrische Ungleichung Fluss Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018960911&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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