Measure theory | Curvature (mathematics)
In mathematics, the curvature of a measure defined on the Euclidean plane R2 is a quantification of how much the measure's "distribution of mass" is "curved". It is related to notions of curvature in geometry. In the form presented below, the concept was introduced in 1995 by the mathematician ; accordingly, it may be referred to as the Melnikov curvature or Menger-Melnikov curvature. Melnikov and Verdera (1995) established a powerful connection between the curvature of measures and the Cauchy kernel. (Wikipedia).
Curvature and Radius of Curvature for a function of x.
This video explains how to determine curvature using short cut formula for a function of x.
From playlist Vector Valued Functions
Curvature and Radius of Curvature for 2D Vector Function
This video explains how to determine curvature using short cut formula for a vector function in 2D.
From playlist Vector Valued Functions
Ex 2A: Find the Curvature of a Space Curve Given by a Vector Function (Cross Product)
This video explains how to determine the curvature of a space curve (helix) at a point given by a vector valued function. Site: http://mathispower4u.com
From playlist Vector Valued Functions
Determining Curvature of a Curve Defined by a Vector Valued Function
This video explain how to determine the curvature of a curve at a given point. http://mathispower4u.wordpress.com/
From playlist Vector Valued Function
The all important concept of curvature. We look at two equations for curvature and introduce the radius of curvature.
From playlist Life Science Math: Vectors
Calculus 3: Vector Calculus in 2D (35 of 39) What is the Sign of Curvature?
Visit http://ilectureonline.com for more math and science lectures! In this video I will show how to identify what is the sign of a curvature. For example, when the angle is getting bigger K is greater than 0, and when the angle is getting smaller K is less than 0. Next video in the seri
From playlist CALCULUS 3 CH 3 VECTOR CALCULUS
Multivariable Calculus | Curvature
We define the notion of the curvature of a vector valued function, prove an equivalent definition, and find the curvature of a circle of radius a. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
GPDE Workshop - Synthetic formulations - Cedric Villani
Cedric Villani IAS/ENS-France February 23, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
Colloquium MathAlp 2016 - Michel Ledoux
Isopérimétrie dans les espaces métriques mesurés Le problème isopérimétrique (à volume donné, minimiser la mesure de bord, et déterminer les ensembles extrémaux), remonte aux temps les plus anciens. Tout à la fois, il peut se formuler de façon générale dans un espace métrique mesuré, et d
From playlist Colloquiums MathAlp
Mokshay Madiman : Minicourse on information-theoretic geometry of metric measure
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 28, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Geometry
A varifold approach to surface approximation and curvature (...) - Buet - Workshop 1 - CEB T1 2019
Buet (Univ. Paris Sud) / 07.02.2019 A varifold approach to surface approximation and curvature estimation on point clouds Joint work with: Gian Paolo Leonardi (Modena) and Simon Masnou (Lyon). We propose a natural framework for the study of surfaces and their different discretizations
From playlist 2019 - T1 - The Mathematics of Imaging
F. Schulze - An introduction to weak mean curvature flow 1
It has become clear in recent years that to understand mean curvature flow through singularities it is essential to work with weak solutions to mean curvature flow. We will give a brief introduction to smooth mean curvature flow and then discuss Brakke flows, their basic properties and how
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Marzieh Eidi (4/8/21): How optimal transport can help us to determine curvature of complex networks?
Title: How optimal transport can help us to determine curvature of complex networks? Abstract: Ollivier Ricci curvature is a notion that originated from Riemannian Geometry and is suitable for applying on different settings from smooth manifolds to discrete structures such as (directed) h
From playlist AATRN 2021
F. Schulze - An introduction to weak mean curvature flow 1 (version temporaire)
It has become clear in recent years that to understand mean curvature flow through singularities it is essential to work with weak solutions to mean curvature flow. We will give a brief introduction to smooth mean curvature flow and then discuss Brakke flows, their basic properties and how
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Areejit Samal (7/25/22): Forman-Ricci curvature: A geometry-inspired measure with wide applications
Abstract: In the last few years, we have been active in the development of geometry-inspired measures for the edge-based characterization of real-world complex networks. In particular, we were first to introduce a discretization of the classical Ricci curvature proposed by R. Forman to the
From playlist Applied Geometry for Data Sciences 2022
Teach Astronomy - Space Curvature
http://www.teachastronomy.com/ General relativity relates the dynamics of the expanding universe to the curvature of space. Thus space curvature is one of the most important things to measure about our universe, but it's an extremely difficult measurement because the curvature is so subtl
From playlist 23. The Big Bang, Inflation, and General Cosmology 2
A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 1 (version temporaire)
The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80ies and was pushed by Cheeger-Colding in the ‘90ies, who investigated the structure of spaces arising as Gromov-Hausdorff limits of smooth Riemannian manifolds
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics