Geometric flow | Differential geometry
In the mathematical fields of differential geometry and geometric analysis, inverse mean curvature flow (IMCF) is a geometric flow of submanifolds of a Riemannian or pseudo-Riemannian manifold. It has been used to prove a certain case of the Riemannian Penrose inequality, which is of interest in general relativity. Formally, given a pseudo-Riemannian manifold (M, g) and a smooth manifold S, an inverse mean curvature flow consists of an open interval I and a smooth map F from I × S into M such that where H is the mean curvature vector of the immersion F(t, ⋅). If g is Riemannian, if S is closed with dim(M) = dim(S) + 1, and if a given smooth immersion f of S into M has mean curvature which is nowhere zero, then there exists a unique inverse mean curvature flow whose "initial data" is f. (Wikipedia).
F. Schulze - Mean curvature flow with generic initial data (version temporaire)
Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric heat equation on the space of hypersurfaces in an ambient Riemannian manifold. It is believed, similar to Ricci Flow in the intrinsic setting, to have the potential to serve as a tool to app
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Marston Morse - Inverse Mean Curvature Flow and Isoperimetric Inequalities
Gerhard Huisken Max-Planck Institute for Gravitational Physics March 20, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
F. Schulze - Mean curvature flow with generic initial data
Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric heat equation on the space of hypersurfaces in an ambient Riemannian manifold. It is believed, similar to Ricci Flow in the intrinsic setting, to have the potential to serve as a tool to app
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Fluid flow for cos(x+y)i + sin(xy)j
From playlist Curl
Yoshihiro Tonegawa: Introduction to Brakke's mean curvature flow (part IV)
The lecture was held within the framework of the Hausdorff Trimester Program: Evolution of Interfaces. Abstract: Among numerous evolution problems involving interface, the mean curvature flow stands out for its simplicity, depth, and width of relevant subfields. The aim of this mini-cours
From playlist Winter School on "Interfaces in Geometry and Fluids"
Yoshihiro Tonegawa: Introduction to Brakke's mean curvature flow (part II)
The lecture was held within the framework of the Hausdorff Trimester Program: Evolution of Interfaces. Abstract: Among numerous evolution problems involving interface, the mean curvature flow stands out for its simplicity, depth, and width of relevant subfields. The aim of this mini-cours
From playlist Winter School on "Interfaces in Geometry and Fluids"
Yoshihiro Tonegawa: Introduction to Brakke's mean curvature flow (part I)
The lecture was held within the framework of the Hausdorff Trimester Program: Evolution of Interfaces. Abstract: Among numerous evolution problems involving interface, the mean curvature flow stands out for its simplicity, depth, and width of relevant subfields. The aim of this mini-cours
From playlist Winter School on "Interfaces in Geometry and Fluids"
Yoshihiro Tonegawa: Introduction to Brakke's mean curvature flow (part III)
The lecture was held within the framework of the Hausdorff Trimester Program: Evolution of Interfaces. Abstract: Among numerous evolution problems involving interface, the mean curvature flow stands out for its simplicity, depth, and width of relevant subfields. The aim of this mini-cours
From playlist Winter School on "Interfaces in Geometry and Fluids"
Relativity 7b1 - slope and curvature
Brief description of the derivative concept from calculus that gives us measures of slope and curvature. These are essential to the theory.
From playlist Relativity - appendix videos
Ancient solutions to geometric flows IV - Panagiota Daskalopoulos
Women and Mathematics: Uhlenbeck Lecture Course Topic: Ancient solutions to geometric flows IV Panagiota Daskalopoulos Affiliation: Columbia University Date: May 24, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Marston Morse - An Isoperimetric Concept for the Mass in General Relativity - Gerhard Huisken
Gerhard Huisken Max-Planck Institute for Gravitational Physics March 20, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
Ben Andrews: Limiting shapes of fully nonlinear flows of convex hypersurfaces
Abstract: I will discuss some questions about the long-time behaviour of hypersurfaces evolving by functions of curvature which are homogeneous of degree greater than 1. ------------------------------------------------------------------------------------------------------------------------
From playlist MATRIX-SMRI Symposium: Singularities in Geometric Flows
Canonical Forms in Geometry and Soliton Theory - Chuu-Lian Terng
Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday Topic: Canonical Forms in Geometry and Soliton Theory Speaker: Chuu-Lian Terng Affiliation: University of California, Irvine Date: September 17, 2022 In this talk, I will explain some applications of
From playlist Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday
Twisted double bilayer graphene and Berry curvature – a tunable system... by Mandar Deshmukh
PROGRAM CLASSICAL AND QUANTUM TRANSPORT PROCESSES : CURRENT STATE AND FUTURE DIRECTIONS (ONLINE) ORGANIZERS: Alberto Imparato (University of Aarhus, Denmark), Anupam Kundu (ICTS-TIFR, India), Carlos Mejia-Monasterio (Technical University of Madrid, Spain) and Lamberto Rondoni (Polytechn
From playlist Classical and Quantum Transport Processes : Current State and Future Directions (ONLINE)2022
Algorithms for motion of networks by weighted mean curvature – Selim Esedoğlu – ICM2018
Mathematics in Science and Technology Invited Lecture 17.13 Algorithms for motion of networks by weighted mean curvature Selim Esedoğlu Abstract: I will report on recent developments in a class of algorithms, known as threshold dynamics, for computing the motion of interfaces by mean cur
From playlist Mathematics in Science and Technology
Pengzi Miao - Recent inequalities on the mass-to-capacity ratio
On an asymptotically flat 3-manifold, both the mass and the capacity have unit of length, and hence their ratio is a dimensionless quantity. In this talk, I will discuss recent work on establishing new inequalities for the mass-to-capacity ratio on manifolds with nonnegative scalar curvatu
From playlist Not Only Scalar Curvature Seminar
Robert Haslhofer: Classification of noncollapsed translators in R^4
Abstract: I will describe our recent classification of noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces. Specifically, we show that every noncollapsed translating hypersurface in R^4 is either R×2d-bowl, or a 3d round bowl, or belongs to the one-pa
From playlist MATRIX-SMRI Symposium: Singularities in Geometric Flows
On dynamical spectral rigidity and determination - Jacopo DeSimoi
Analysis Seminar Topic: On dynamical spectral rigidity and determination Speaker: Jacopo De Simoi Affiliation: University of Toronto Date: February 10, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Fluid flow with four points of curl interest
From playlist Curl
Panagiota Daskalopoulos: 1/3 Ancient Solutions to Geometric Flows [2017]
Ancient Solutions to Geometric Flows Speaker: Panagiota Daskalopoulos, Columbia University Date and Time: Tuesday, October 3, 2017 - 4:30pm to 5:30pm Location: Fields Institute, Room 230 Abstract: Some of the most important problems in geometricgeometric flowsflows are related to the un
From playlist Mathematics