Lectures on mean curvature flows:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2002
|
| Series: | AMS, IP studies in advanced mathematics
32 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | ix, 150 p. 27 cm |
| ISBN: | 0821833111 |
Staff View
MARC
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| 100 | 1 | |a Zhu, Xi-Ping |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lectures on mean curvature flows |c Xi-Ping Zhu |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2002 | |
| 300 | |a ix, 150 p. |b 27 cm | ||
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| 650 | 4 | |a Flows (Differentiable dynamical systems) | |
| 650 | 4 | |a Surfaces of constant curvature | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1
The curve shortening flow for convex curves
1
1.1
Shrinking to a Point
......................... 2
1.2
Asymptotic Behavior
......................... 6
2
The Short Time Existence and The Evolution Equation of Cur¬
vatures
15
2.1
Local Existence
............................ 17
2.2
Evolution of Metric and Curvature
................. 18
2.3
Pinching Estimate
.......................... 20
3
Contraction of Convex Hypersurfaces
25
3.1
Some Facts on Convex Hypersurface
................ 25
3.2
MCF FOR CONVEX HYPERSURFACES
............. 29
4
Monotonicity
and Self-Similar Solutions
35
4.1
Type I Limits
............................. 35
4.2
The Classification of Self-similar Solutions
............. 39
5
Evolution of Embedded Curves or Surfaces (I)
47
5.1
Isoperimetrie Estimates
....................... 48
5.2
Blow-up Argument
.......................... 50
5.3
Convexity Theorem
.......................... 52
6
Evolution of Embedded Curves and Surfaces (II)
55
6.1
Curves with Finite Total Absolute Curvature
........... 55
6.2
Long Time Existence for Complete Curves
............. 60
7
Evolution of Embedded Curves and Surfaces (III)
67
7.1
The Evolution Equation of Gradient Function
........... 68
7.2
Gradient Estimates
.......................... 69
7.3
Curvature Estimates
......................... 71
7.4
Long Time Existence for Entire Graphs
.............. 75
8
Convexity Estimates for Mean Convex Surfaces
77
8.1
Evolution Equations
......................... 78
8.2
D> Estimates
............................. 80
8.3
De Giorgi
Iteration Argument
.................... 84
vi
CONTENTS
9
Li-Yau Estimates and Type II Singularities
89
9.1
Translating Soliton
.......................... 90
9.2
Li-Yau Type Inequality
....................... 91
9.3
Type II Limits
............................ 97
10
The Mean Curvature Flow in Riemannian Manifolds
101
10.1
Hypersurfaces in Riemannian Manifolds
..............101
10.2
Evolution Equations
.........................104
11
Contracting Convex Hypersurfaces in Riemannian Manifolds
109
11.1
The Pinching Estimates
.......................109
11.2
A Geometric Lemma
.........................112
11.3
Huisken Theorem
...........................115
12
Definition of Center of Mass for Isolated Gravitating Systems
123
12.1
Approximately Round Surfaces
...................124
12.2
Existence of Constant Mean Curvature Surfaces
.....128
12.3
Center of Gravity
...........................137
References
145
Index
149
|
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| id | DE-604.BV014629463 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:04:33Z |
| institution | BVB |
| isbn | 0821833111 |
| language | English |
| lccn | 2002027977 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009940446 |
| oclc_num | 50251982 |
| open_access_boolean | |
| owner | DE-384 DE-355 DE-BY-UBR DE-188 |
| owner_facet | DE-384 DE-355 DE-BY-UBR DE-188 |
| physical | ix, 150 p. 27 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | AMS, IP studies in advanced mathematics |
| series2 | AMS, IP studies in advanced mathematics |
| spelling | Zhu, Xi-Ping Verfasser aut Lectures on mean curvature flows Xi-Ping Zhu Providence, R.I. American Mathematical Society 2002 ix, 150 p. 27 cm txt rdacontent n rdamedia nc rdacarrier AMS, IP studies in advanced mathematics 32 Includes bibliographical references and index Flows (Differentiable dynamical systems) Surfaces of constant curvature Mittlere Krümmung (DE-588)4235959-4 gnd rswk-swf Krümmungsfluss (DE-588)4618875-7 gnd rswk-swf Mittlere Krümmung (DE-588)4235959-4 s Krümmungsfluss (DE-588)4618875-7 s DE-604 AMS, IP studies in advanced mathematics 32 (DE-604)BV011103148 32 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940446&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhu, Xi-Ping Lectures on mean curvature flows AMS, IP studies in advanced mathematics Flows (Differentiable dynamical systems) Surfaces of constant curvature Mittlere Krümmung (DE-588)4235959-4 gnd Krümmungsfluss (DE-588)4618875-7 gnd |
| subject_GND | (DE-588)4235959-4 (DE-588)4618875-7 |
| title | Lectures on mean curvature flows |
| title_auth | Lectures on mean curvature flows |
| title_exact_search | Lectures on mean curvature flows |
| title_full | Lectures on mean curvature flows Xi-Ping Zhu |
| title_fullStr | Lectures on mean curvature flows Xi-Ping Zhu |
| title_full_unstemmed | Lectures on mean curvature flows Xi-Ping Zhu |
| title_short | Lectures on mean curvature flows |
| title_sort | lectures on mean curvature flows |
| topic | Flows (Differentiable dynamical systems) Surfaces of constant curvature Mittlere Krümmung (DE-588)4235959-4 gnd Krümmungsfluss (DE-588)4618875-7 gnd |
| topic_facet | Flows (Differentiable dynamical systems) Surfaces of constant curvature Mittlere Krümmung Krümmungsfluss |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940446&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011103148 |
| work_keys_str_mv | AT zhuxiping lecturesonmeancurvatureflows |