Lectures on differential geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Chinese |
| Published: |
Boston [u.a.]
Internat. Press
1994
|
| Series: | Conference proceedings and lecture notes in geometry and topology
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | V, 414 S. |
| ISBN: | 1571460128 |
Staff View
MARC
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| 100 | 1 | |a Schoen, Richard Melvin |d 1950- |e Verfasser |0 (DE-588)1089595468 |4 aut | |
| 245 | 1 | 0 | |a Lectures on differential geometry |c R. Schoen ; S.-T. Yau |
| 264 | 1 | |a Boston [u.a.] |b Internat. Press |c 1994 | |
| 300 | |a V, 414 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Conference proceedings and lecture notes in geometry and topology |v 1 | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804124936202092544 |
|---|---|
| adam_text | Table
of
Contents
Preface for the English Translation
.......................................
p.
і
Translation of Original Preface
..........................................
p. ii
Chapter I: Comparison Theorems and Gradient Estimates
...............
p.
1
§1.
Comparison Theorems
...........................................
p.
1
§2.
Splitting Theorem
..............................................
p.
12
§3.
Gradient Estimate
.............................................
p.
17
§4.
Complete Riemannian Manifolds of Non-Negative
Ricci
Curvature
.............................................
p.
23
Chapter II: Harmonic Functions on Manifolds
with Negative Curvature
.......................................
p.
31
§1.
Geometric Boundary
5(00)
and Solvability of
the Dirichlet Problem
.......................................
p.
32
§2.
Harnack Inequality and
Poisson
Kernel
.........................
p.
41
§3.
Martin Boundary and Martin Integral Representation
...........
p.
50
§4.
Proof of Harnack Inequalities
...................................
p.
55
§5.
Harmonic Functions on More General Manifolds
................
p.
65
§6.
Mean Value Inequality for Subharmonic Functions
..............
p.
75
Appendix to Chapter II: The Existence of an Entire
Green s Function
............................................
p.
81
Chapter III: Eigenvalue Problems
......................................
p.
87
§1.
Basic Properties of Eigenvalues
.................................
p.
87
§2.
The Heat Kernel of Riemannian Manifolds
......................
p.
93
§3.
Upper Bounds for the First Eigenvalue
λχ
.....................
p.
104
§4.
Lower Bounds for the First Eigenvalue Aj
.....................
p.
106
§5.
Estimates on Higher Eigenvalues
..............................
p.
117
§6.
Nodal Sets and Multiplicities of Eigenvalues
...................
p.
122
§7.
Gaps Between Eigenvalues
....................................
p.
128
§8.
Eigenvalue Problems for Surfaces
..............................
p.
134
Chapter IV: Heat Kernel on Riemannian Manifolds
...................
p.
155
§1.
Gradient Estimates of Heat Kernel
............................
p.
155
§2.
Harnack Inequality and Estimates for the Heat Kernel
.........
p.
163
§3.
Applications of the Estimates for Heat Kernel
.................
p.
176
Chapter V:
Conformai
Deformation of Scalar Curvatures
..............
p.
183
§1.
The Two-Dimensional Case
...................................
p.
187
§2.
Yamabe Problem and
Conformai
Invariant
λ(Μ)
..............
p.
199
§3.
Conformai
Normal Coordinates and Asymptotic Expansion
of Green s Function
........................................
P·
207
§4.
The Resolution of Yamabe Problem
...........................
p.
219
Appendix to Chapter V: Best Constant in the Sobolev Inequality
.
p.
224
Chapter VI: Locally Conformally Flat Manifolds
......................
p.
231
§1.
Conformai
Transformations and Locally Conformally
Flat Manifolds
.............................................
p.
232
§2.
Conformai
Invariants
..........................................
p.
239
§3.
Embeddings of Locally Conformally Flat Manifolds into Sn
....
p.
253
§4.
Topology of Locally Conformally Flat Manifolds
...............
p.
263
§5.
P.D.E. Aspects of the Theory
.................................
p.
273
Chapter
VII:
Problem Section
........................................
p.
277
§1.
Curvature and the Topology of Manifolds
......................
p.
278
§11.
Curvature and the Complex Structure
.........................
p.
285
§111.
Submanifolds
................................................
p.
288
§IV. The Spectrum
...............................................
p.
293
§V. Problems Related to Geodesies
................................
p.
296
fjVI. Minimal Submanifolds
.......................................
p.
297
§VII. General Relativity and the Yang-Mills Equation
.............
p.
303
Bibliography
......................................................
p.
305
Chapter
VIII:
Nonlinear Analysis in Geometry
........................
p.
315
§1.
Eigenvalues and Harmonic Functions
..........................
p.
318
§2.
Yamabe s Equation and Conformally Flat Manifolds
...........
p.
324
§3.
Harmonic Maps
...............................................
p.
326
§4. Minimal Submanifolds ........................................
p.
330
§5. Kahler
Geometry
..............................................
p.
335
§6.
Canonical Metrics over Complex Manifolds
....................
p.
344
References
........................................................
p.
358
Chapter IX: Open Problems in Differential Geometry
.................
p.
365
§1.
Metric Geometry
..............................................
p.
365
§11.
Classical Euclidean Geometry
.................................
p.
372
§111.
Partial Differential Equations
................................
p.
380
§IV.
Kahler
Geometry
............................................
p.
387
References
........................................................
p.
405
Bibliography
...........................................................
p.
411
Index:
................................................................
p.
415
|
| any_adam_object | 1 |
| author | Schoen, Richard Melvin 1950- Yau, Shing-Tung 1949- |
| author_GND | (DE-588)1089595468 (DE-588)111571952 |
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| author_role | aut aut |
| author_sort | Schoen, Richard Melvin 1950- |
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| building | Verbundindex |
| bvnumber | BV010502023 |
| classification_rvk | SD 1984 SK 370 |
| classification_tum | MAT 530f |
| ctrlnum | (OCoLC)472300771 (DE-599)BVBBV010502023 |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)1071861417 Konferenzschrift 1984 Princeton NJ gnd-content |
| genre_facet | Konferenzschrift 1984 Princeton NJ |
| id | DE-604.BV010502023 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:53:35Z |
| institution | BVB |
| isbn | 1571460128 |
| language | English Chinese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006998685 |
| oclc_num | 472300771 |
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| owner_facet | DE-384 DE-703 DE-29T DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-634 DE-11 DE-188 DE-83 |
| physical | V, 414 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Internat. Press |
| record_format | marc |
| series | Conference proceedings and lecture notes in geometry and topology |
| series2 | Conference proceedings and lecture notes in geometry and topology |
| spelling | Schoen, Richard Melvin 1950- Verfasser (DE-588)1089595468 aut Lectures on differential geometry R. Schoen ; S.-T. Yau Boston [u.a.] Internat. Press 1994 V, 414 S. txt rdacontent n rdamedia nc rdacarrier Conference proceedings and lecture notes in geometry and topology 1 Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1984 Princeton NJ gnd-content Differentialgeometrie (DE-588)4012248-7 s 1\p DE-604 Yau, Shing-Tung 1949- Verfasser (DE-588)111571952 aut Conference proceedings and lecture notes in geometry and topology 1 (DE-604)BV010502014 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006998685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schoen, Richard Melvin 1950- Yau, Shing-Tung 1949- Lectures on differential geometry Conference proceedings and lecture notes in geometry and topology Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)1071861417 |
| title | Lectures on differential geometry |
| title_auth | Lectures on differential geometry |
| title_exact_search | Lectures on differential geometry |
| title_full | Lectures on differential geometry R. Schoen ; S.-T. Yau |
| title_fullStr | Lectures on differential geometry R. Schoen ; S.-T. Yau |
| title_full_unstemmed | Lectures on differential geometry R. Schoen ; S.-T. Yau |
| title_short | Lectures on differential geometry |
| title_sort | lectures on differential geometry |
| topic | Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Differentialgeometrie Konferenzschrift 1984 Princeton NJ |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006998685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010502014 |
| work_keys_str_mv | AT schoenrichardmelvin lecturesondifferentialgeometry AT yaushingtung lecturesondifferentialgeometry |