Advanced basics of Riemannian geometry 2 - TIB AV-Portal

Advanced basics of Riemannian geometry 2

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Institut Fourier

Richard, Thomas

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Title

Advanced basics of Riemannian geometry 2

Title of Series

Summer School 2021 - Curvature Constraints and Spaces of Metrics

Number of Parts

48

Author

Richard, Thomas

License

CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.5446/66204 (DOI)

Publisher

Institut Fourier

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Abstract

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the Bochner formula and basics of Ricci flow.

Series

Summer School 2021 - Curvature Constraints and Spaces of Metrics45 / 48

1

1:02:14

Boundary regularity and stability under lower Ricci bounds

2

1:44:17

Metric measure spaces satisfying Ricci curvature lower bounds 2

3

1:46:05

Metric measure spaces satisfying Ricci curvature lower bounds 1

4

1:41:39

Metric measure spaces satisfying Ricci curvature lower bounds 3

5

1:34:17

CAT(k)-spaces 2

6

1:35:15

CAT(k)-spaces 3

7

1:20:15

CAT(k)-spaces 4

8

1:21:33

Intrinsic Flat and Gromov-Hausdorff Convergence 1

9

1:08:00

Limits of Riemannian manifolds satisfying a uniform Kato condition

10

1:37:10

Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 1

11

1:25:56

Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 3

12

1:28:24

Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 2

13

1:28:18

Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 4

14

56:54

On the essential minimal volume of Einstein 4-manifolds

15

1:33:39

CAT(k)-spaces 1

16

52:02

Convex subsets in generic manifolds

17

1:44:27

Metric measure spaces satisfying Ricci curvature lower bounds 4

18

1:14:45

Time-like Ricci curvature bounds via optimal transport

19

1:25:35

What is the (essential) minimal volume? 4

20

1:26:58

What is the (essential) minimal volume? 3

21

1:23:09

What is the (essential) minimal volume? 2

22

1:03:35

Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions

23

1:36:19

Intrinsic Flat and Gromov-Hausdorff Convergence 4

24

1:43:32

Intrinsic Flat and Gromov-Hausdorff Convergence 3

25

1:01:56

Mean curvature flow with generic initial data

26

1:13:19

Compactness and partial regularity theory of Ricci flows in higher dimensions

27

54:16

Recent Intrinsic Flat Convergence Theorems

28

1:03:55

Noncollapsed degeneration and desingularization of Einstein 4-manifolds

29

1:02:34

Steady gradient Ricci solitons with positive curvature

30

1:32:05

What is the (essential) minimal volume? 1

31

1:00:09

Harmonic map methods in spectral geometry

32

1:23:02

An introduction to weak mean curvature flow 3

33

1:26:29

An introduction to weak mean curvature flow 1

34

1:22:00

An introduction to weak mean curvature flow 4

35

1:27:36

An introduction to weak mean curvature flow 2

36

1:01:03

Knots, minimal surfaces and J-holomorphic curves

37

28:19

Topological rigidity and positive scalar curvature

38

1:15:12

Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem

39

1:00:09

Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow

40

1:32:42

Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 3

41

57:40

Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 4

42

1:31:25

Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 2

43

1:31:43

Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 1

44

1:30:44

Advanced basics of Riemannian geometry 1

45

1:21:33

Advanced basics of Riemannian geometry 2

46

1:30:20

Advanced basics of Riemannian geometry 3

47

1:34:51

Advanced basics of Riemannian geometry 4

48

1:32:53

Intrinsic Flat and Gromov-Hausdorff Convergence 2

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