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
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
F. Schulze - An introduction to weak mean curvature flow 2
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
(Non)uniqueness questions in mean curvature flow - Lu Wang
Variational Methods in Geometry Seminar Topic: (Non)uniqueness questions in mean curvature flow Speaker: Lu Wang Affiliation: University of Wisconsin–Madison; Member, School of Mathematics Date: January 22, 2019 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
F. Schulze - An introduction to weak mean curvature flow 2 (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
F. Schulze - An introduction to weak mean curvature flow 4 (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
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
F. Schulze - An introduction to weak mean curvature flow 3 (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
P. Burkhardt-Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow (vt)
We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starti
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
P. Burkhardt-Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow
We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starti
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Paula Burkhardt-Guim - Lower scalar curvature bounds for $C^0$ metrics: a Ricci flow approach
We describe some recent work that has been done to generalize the notion of lower scalar curvature bounds to C^0 metrics, including a localized Ricci flow approach. In particular, we show the following: that there is a Ricci flow definition which is stable under greater-than-second-order p
From playlist Not Only Scalar Curvature Seminar
R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 1
I will present recent work with Kleiner in which we verify two topological conjectures using Ricci flow. First, we classify the homotopy type of every 3-dimensional spherical space form. This proves the Generalized Smale Conjecture and gives an alternative proof of the Smale Conjecture, wh
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Convergent Evolving Surface Finite Element Algorithms for Geometric Evolution Equations
Professor Christian Lubich University of Tübingen, Germany
From playlist Distinguished Visitors Lecture Series
R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 1 (vt)
I will present recent work with Kleiner in which we verify two topological conjectures using Ricci flow. First, we classify the homotopy type of every 3-dimensional spherical space form. This proves the Generalized Smale Conjecture and gives an alternative proof of the Smale Conjecture, wh
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
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
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
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"
Seminar In the Analysis and Methods of PDE (SIAM PDE): Felix Otto
Date: September 3, 2020 Speaker: Felix Otto Title: The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows Abstract: Flow of interfaces by mean curvature, in its multi-phase version, was first formulated in the context of grain growth in polycrystalline
From playlist Seminar In the Analysis and Methods of PDE (SIAM PDE)