Manifolds #5: Tangent Space (part 1)
Today, we introduce the notion of tangent vectors and the tangent vector space at a point on a manifold.
From playlist Manifolds
What is a Manifold? Lesson 6: Topological Manifolds
Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.
From playlist What is a Manifold?
What is a Manifold? Lesson 2: Elementary Definitions
This lesson covers the basic definitions used in topology to describe subsets of topological spaces.
From playlist What is a Manifold?
Julien Duval - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties 2/2
An almost complex manifold is hyperbolic if it does not contain any entire curve. We start characterizing hyperbolic compact almost complex manifolds. These are the ones whose holomorphic discs satisfy a linear isoperimetric inequality. Then we prove the almost complex version of the Greee
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Julien Duval - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties 1/2
An almost complex manifold is hyperbolic if it does not contain any entire curve. We start characterizing hyperbolic compact almost complex manifolds. These are the ones whose holomorphic discs satisfy a linear isoperimetric inequality. Then we prove the almost complex version of the Greee
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Manifolds 1.1 : Basic Definitions
In this video, I give the basic intuition and definitions of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Manifolds
I define topological manifolds. Motivated by the prospect of calculus on topological manifolds, I introduce smooth manifolds. At the end I point out how one needs to change the definitions, to obtain C^1 or even complex manifolds. To learn more about manifolds, see Lee's "Introduction to
From playlist Differential geometry
What is a Manifold? Lesson 3: Separation
He we present some alternative topologies of a line interval and then discuss the notion of separability. Note the error at 4:05. Sorry! If you are viewing this on a mobile device, my annotations are not visible. This is due to a quirck of YouTube.
From playlist What is a Manifold?
A. Song - What is the (essential) minimal volume? 4 (version temporaire)
I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of resu
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
A. Song - What is the (essential) minimal volume? 4
I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of resu
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
R. Perales - Recent Intrinsic Flat Convergence Theorems
Given a closed and oriented manifold M and Riemannian tensors g0, g1, ... on M that satisfy g0 gj, vol(M, gj)→vol (M, g0) and diam(M, gj)≤D we will see that (M, gj) converges to (M, g0) in the intrinsic flat sense. We also generalize this to the non-empty bundary setting. We remark that u
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
R. Perales - Recent Intrinsic Flat Convergence Theorems (version temporaire)
Given a closed and oriented manifold M and Riemannian tensors g0, g1, ... on M that satisfy g0 gj, vol(M, gj)→vol (M, g0) and diam(M, gj)≤D we will see that (M, gj) converges to (M, g0) in the intrinsic flat sense. We also generalize this to the non-empty bundary setting. We remark that u
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Christina Sormani - Sequences of manifolds with lower bounds on their scalar curvature
If one has a weakly converging sequence of manifolds with a uniform lower bound on their scalar curvature, what properties of scalar curvature persist on the limit space? What additional hypotheses might be added to provide stronger controls on the limit space? What hypotheses are requ
From playlist Not Only Scalar Curvature Seminar
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 4 (version temporaire)
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 4
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Christina Sormani: A Course on Intrinsic Flat Convergence part 4
The lecture was held within the framework of the Hausdorff Trimester Program: Optimal Transportation and the Workshop: Winter School & Workshop: New developments in Optimal Transport, Geometry and Analysis
From playlist HIM Lectures 2015
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 3 (version temporaire)
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 3
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Correction of Manifolds 1.5 : Manifolds with Boundary
Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet Playlist :
From playlist Manifolds