Lecture notes on mean curvature flow:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel
Birkhäuser
2011
|
| Series: | Progress in mathematics
290 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 166 S. |
| ISBN: | 9783034801447 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lecture notes on mean curvature flow |c Carlo Mantegazza |
| 264 | 1 | |a Basel |b Birkhäuser |c 2011 | |
| 300 | |a XII, 166 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 830 | 0 | |a Progress in mathematics |v 290 |w (DE-604)BV000004120 |9 290 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Foreword
............................................... ix
1 Definition and Short
Time Existence
1.1
Notation and Preliminaries
............................ 1
1.2
First Variation of the Area Functional
.................... 5
L3 The Mean Curvature Flow
............................ 7
1.4
Examples
......................................... 11
1.5
Short Time Existence of the Flow
....................... 18
1.6
Other Second-order Flows
............................. 23
2
Evolution of Geometric Quantities
2.1
Maximum Principle
................................. 25
2.2
Comparison Principle
................................ 28
2.3
Evolution of Curvature
............................... 32
2.4
Consequences of Evolution Equations
..................... 36
2.5
Convexity
Invariance
................................ 42
3
Monotonicity
Formula and Type I Singularities
3.1
The
Monotonicity
Formula for Mean Curvature Flow
......... 49
3.2
Type I Singularities and the Rescaling Procedure
............ 52
3.3
Analysis of Singularities
.............................. 69
3.4
Hypersurfaces with
Nonnegative
Mean Curvature
............ 74
3.5
Embedded Closed Curves in the Plane
.................... 84
4
Type II Singularities
4.1
Hamilton s Blow-up
................................. 86
4.2
Hypersurfaces with
Nonnegative
Mean Curvature
............ 95
4.3
The Special Case of Curves
............................ 98
4.4
Hamilton s Harnack Estimate for Mean Curvature Flow
....... 100
4.5
Embedded Closed Curves in the Plane
.................... 105
viii Contents
5
Conclusions and Research Directions
5.1
Curves in the Plane
................................. 115
5.2
Hypersurfaces
..................................... 116
5.3
Mean Curvature Flow with Surgeries
..................... 117
5.4
Some Problems and Research Directions
................... 121
Appendix
A
Quasilinear
Parabolic Equations on Manifolds
A.I The Linear Case
.................................... 124
A.2 Regularity in the Linear Case
.......................... 128
A.3 The General Case
................................... 136
В
Interior Estimates of
Ecker
and Huisken
...................... 145
С
Hamilton s Maximum Principle for Tensors
.................... 147
D
Hamilton s Matrix Li-Yau-Harnack Inequality in K™
............. 149
E Abresch
and
Langer
Classification
........................... 151
F
Important Results without Proof in the Book
.................. 155
Bibliography
............................................ 157
Index
................................................. 165
|
| any_adam_object | 1 |
| author | Mantegazza, Carlo 1970- |
| author_GND | (DE-588)1014980631 |
| author_facet | Mantegazza, Carlo 1970- |
| author_role | aut |
| author_sort | Mantegazza, Carlo 1970- |
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| bvnumber | BV039555915 |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)752226900 (DE-599)BVBBV039555915 |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-10T00:06:11Z |
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| isbn | 9783034801447 |
| language | English |
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| physical | XII, 166 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Mantegazza, Carlo 1970- Verfasser (DE-588)1014980631 aut Lecture notes on mean curvature flow Carlo Mantegazza Basel Birkhäuser 2011 XII, 166 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 290 Dynamisches System (DE-588)4013396-5 gnd rswk-swf Fluss Mathematik (DE-588)4489499-5 gnd rswk-swf Mittlere Krümmung (DE-588)4235959-4 gnd rswk-swf Fluss Mathematik (DE-588)4489499-5 s Mittlere Krümmung (DE-588)4235959-4 s Dynamisches System (DE-588)4013396-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-0348-0145-4 Progress in mathematics 290 (DE-604)BV000004120 290 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024407700&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mantegazza, Carlo 1970- Lecture notes on mean curvature flow Progress in mathematics Dynamisches System (DE-588)4013396-5 gnd Fluss Mathematik (DE-588)4489499-5 gnd Mittlere Krümmung (DE-588)4235959-4 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4489499-5 (DE-588)4235959-4 |
| title | Lecture notes on mean curvature flow |
| title_auth | Lecture notes on mean curvature flow |
| title_exact_search | Lecture notes on mean curvature flow |
| title_full | Lecture notes on mean curvature flow Carlo Mantegazza |
| title_fullStr | Lecture notes on mean curvature flow Carlo Mantegazza |
| title_full_unstemmed | Lecture notes on mean curvature flow Carlo Mantegazza |
| title_short | Lecture notes on mean curvature flow |
| title_sort | lecture notes on mean curvature flow |
| topic | Dynamisches System (DE-588)4013396-5 gnd Fluss Mathematik (DE-588)4489499-5 gnd Mittlere Krümmung (DE-588)4235959-4 gnd |
| topic_facet | Dynamisches System Fluss Mathematik Mittlere Krümmung |
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