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0:32:22

Lesson 44: A metric characterization of Carnot groups

0:54:37

Lesson 43: Isometrically homogeneous geodesic manifolds

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Lesson 42: Rank-one symmetric spaces as Heintze groups

0:46:22

Lesson 41: Negatively curved homogeneous manifolds

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Lesson 40: Equicontinuity of Carnot-Carathéodory distances

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Lesson 39: Proof of convergence of Carnot-Carathéodory structures.

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Lesson 38: Limits of CC bundle structures

0:44:36

Lesson 37: A discussion on Mitchell's theorem

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Lesson 36: An example: the asymptotic cone of the Riemannian Heisenberg group

0:44:38

Lesson 35: Limits of Carnot-Carathéodory distances

0:41:00

Lesson 34: Tangent spaces and asymptotic spaces

0:36:01

Lesson 33: Limits of metric spaces

0:15:35

Lesson 32: a biLipschitz non-embeddability consequence

0:43:01

Lesson 31: Proof of Pansu's Rademacher Theorem

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Lesson 30: Pansu's Rademacher Theorem for curves

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Lesson 29: Differentiability of Lipschitz maps between Carnot groups

0:23:38

Lesson 28: Measures on Carnot groups

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Lesson 27: Examples of Carnot groups and Carnot algebras

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Lesson 26: Dilations on Carnot groups

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Lesson 25: Introduction to Carnot groups

0:32:44

Lesson 24: Exponential coordinates on simply connected nilpotent Lie groups

0:41:50

Lesson 23: Nilpotent Lie groups

0:35:18

Lesson 22: Extremal equations of energy minimizers

0:32:30

Lesson 21: First-order necessary conditions for energy minimizers