Minimal surfaces | Differential geometry of surfaces | Differential geometry
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However, the term is used for more general surfaces that may self-intersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see minimal surface of revolution): the standard definitions only relate to a local optimum, not a global optimum. (Wikipedia).
Complex surfaces 2: Minimal surfaces
This talk is part of a series about complex surfaces, and explains what minimal surfaces are. A minimial surfaces is one that cannot be obtained by blowing up a nonsingular surfaces at a point. We explain why every surface is birational to a minimal nonsingular projective surface. We disc
From playlist Algebraic geometry: extra topics
Minimal Surfaces—The Shapes That Help Us Understand Black Holes
In this video I talk about minimal surfaces and how you can do your own experiment to prove if something is a minimal surface. I talk about why minimal surfaces are important in math and physics and show you some neat experiments to make several minimal surfaces at home The STL file for t
From playlist Amazing 3D Printed Objects
L. Mazet - Some aspects of minimal surface theory (Part 1)
In a Riemannian 3-manifold, minimal surfaces are critical points of the area functional and can be a useful tool to understand the geometry and the topology of the ambient manifold. The aim of these lectures is to give some basic definitions about minimal surface theory and present some re
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
L. Mazet - Some aspects of minimal surface theory (Part 4)
In a Riemannian 3-manifold, minimal surfaces are critical points of the area functional and can be a useful tool to understand the geometry and the topology of the ambient manifold. The aim of these lectures is to give some basic definitions about minimal surface theory and present some re
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
L. Mazet - Some aspects of minimal surface theory (Part 3)
In a Riemannian 3-manifold, minimal surfaces are critical points of the area functional and can be a useful tool to understand the geometry and the topology of the ambient manifold. The aim of these lectures is to give some basic definitions about minimal surface theory and present some re
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
L. Mazet - Some aspects of minimal surface theory (Part 5)
In a Riemannian 3-manifold, minimal surfaces are critical points of the area functional and can be a useful tool to understand the geometry and the topology of the ambient manifold. The aim of these lectures is to give some basic definitions about minimal surface theory and present some re
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
L. Mazet - Some aspects of minimal surface theory (Part 2)
In a Riemannian 3-manifold, minimal surfaces are critical points of the area functional and can be a useful tool to understand the geometry and the topology of the ambient manifold. The aim of these lectures is to give some basic definitions about minimal surface theory and present some re
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
L. Mazet - Minimal hypersurfaces of least area
In this talk, I will present a joint work with H. Rosenberg where we give a characterization of the minimal hypersurface of least area in any Riemannian manifold. As a consequence, we give a lower bound for the area of a minimal surface in a hyperbolic 3-manifold.
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
F. Coda Marques - Morse theory and the volume spectrum
In this talk I will survey recent developments on the existence theory of closed minimal hypersurfaces in Riemannian manifolds, including a Morse-theoretic existence result for the generic case.
From playlist 70 ans des Annales de l'institut Fourier
Zero mean curvature surfaces in Euclidean and Lorentz-Minkowski....(Lecture 1) by Shoichi Fujimori
Discussion Meeting Discussion meeting on zero mean curvature surfaces (ONLINE) Organizers: C. S. Aravinda and Rukmini Dey Date: 07 July 2020 to 15 July 2020 Venue: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conduct
From playlist Discussion Meeting on Zero Mean Curvature Surfaces (Online)
J. Fine - Knots, minimal surfaces and J-holomorphic curves
I will describe work in progress, parts of which are joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I will explain how one can count minimal surfaces in hyperbolic 4-space which have ideal boundary equal to L, and in this way obtain a knot invariant. In other words the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
J. Fine - Knots, minimal surfaces and J-holomorphic curves (version temporaire)
I will describe work in progress, parts of which are joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I will explain how one can count minimal surfaces in hyperbolic 4-space which have ideal boundary equal to L, and in this way obtain a knot invariant. In other words the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Introduction to Minimal surfaces by Rukmini Dey
SUMMER SCHOOL FOR WOMEN IN MATHEMATICS AND STATISTICS POPULAR TALKS (TITLE AND ABSTRACT) June 22, Wednesday, 15:45 - 16:45 hrs Rukmini Dey (ICTS, India) Title: Introduction to Minimal surfaces Abstract: In this talk I will introduce zero mean curvature surfaces, called minimal surface
From playlist Summer School for Women in Mathematics and Statistics - 2022
Existence of infinitely many minimal hypersurfaces in closed manifolds - Antoine Song
Variational Methods in Geometry Seminar Topic: Existence of infinitely many minimal hypersurfaces in closed manifolds Speaker: Antoine Song Affiliation: Princeton University Date: October 23, 2018 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
New and old results in the classical theory of…surfaces in Euclidean 3-space R^3 - Bill Meeks
Members' Seminar Topic: New and old results in the classical theory of minimal and constant mean curvature surfaces in Euclidean 3-space R^3 Speaker: Bill Meeks Affiliation: University of Massachusetts Amherst Date: October 22, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
On the existence of minimal Heegaard splittings - Dan Ketover
Variational Methods in Geometry Seminar Topic: On the existence of minimal Heegaard splittings Speaker: Dan Ketover Affiliation: Princeton University; Member, School of Mathematics Date: Oct 2, 2018 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Foliations of 3-manifolds of Positive Scalar Curvature by Surfaces of Controlled Size
Yevgeny Liokumovich (University of Toronto) Abstract: Let M be a compact 3-manifold with scalar curvature at least 1. We show that there exists a Morse function f on M, such that every connected component of every fiber of f has genus, area and diameter bounded by a universal constant. T
From playlist Informal Geometric Analysis Seminar
Minimal surfaces in R^3 and Maximal surfaces in L^3 (Lecture 3) by Pradip Kumar
ORGANIZERS : C. S. Aravinda and Rukmini Dey DATE & TIME : 16 June 2018 to 25 June 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore This workshop on geometry and topology for lecturers is aimed for participants who are lecturers in universities/institutes and colleges in India. This w
From playlist Geometry and Topology for Lecturers
Surface Integral of a Vector Field - Part 1
http://mathispower4u.wordpress.com/
From playlist Surface Integrals