Harmonic functions | Differential forms | Riemann surfaces
In mathematics, differential forms on a Riemann surface are an important special case of the general theory of differential forms on smooth manifolds, distinguished by the fact that the conformal structure on the Riemann surface intrinsically defines a Hodge star operator on 1-forms (or differentials) without specifying a Riemannian metric. This allows the use of Hilbert space techniques for studying function theory on the Riemann surface and in particular for the construction of harmonic and holomorphic differentials with prescribed singularities. These methods were first used by in his variational approach to the Dirichlet principle, making rigorous the arguments proposed by Riemann. Later found a direct approach using his method of orthogonal projection, a precursor of the modern theory of elliptic differential operators and Sobolev spaces. These techniques were originally applied to prove the uniformization theorem and its generalization to planar Riemann surfaces. Later they supplied the analytic foundations for the harmonic integrals of . This article covers general results on differential forms on a Riemann surface that do not rely on any choice of Riemannian structure. (Wikipedia).
Solve the general solution for differentiable equation with trig
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
Examples of curvatures of surfaces | Differential Geometry 30 | NJ Wildberger
We review the formulas for the curvature of a surface we derived/discussed in the last lecture, and then give explicit examples of how these formulas work out in special cases. The formulas were given in several roughly equivalent forms, applying to different situations. The first applied
From playlist Differential Geometry
Find the particular solution given the conditions and second derivative
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations
How to solve a differentialble equation by separating the variables
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
Differential Equations | Variation of Parameters.
We derive the general form for a solution to a differential equation using variation of parameters. http://www.michael-penn.net
From playlist Differential Equations
How to solve differentiable equations with logarithms
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
Introduction to Differential Equations
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to Differential Equations - The types of differential equations, ordinary versus partial. - How to find the order of a differential equation.
From playlist Differential Equations
Quadratic differentials and measured foliations on Riemann surfaces by Subhojoy Gupta
Program : Integrable? ?systems? ?in? ?Mathematics,? ?Condensed? ?Matter? ?and? ?Statistical? ?Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan L
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
C. Leininger - Teichmüller spaces and pseudo-Anosov homeomorphism (Part 2)
I will start by describing the Teichmuller space of a surface of finite type from the perspective of both hyperbolic and complex structures and the action of the mapping class group on it. Then I will describe Thurston's compactification of Teichmuller space, and state his classification t
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Hodge Theory -- From Abel to Deligne - Phillip Griffiths
Phillip Griffiths School of Mathematics, Institute for Advanced Study October 14, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Michael Wolf - Sheared Pleated surfaces and Limiting Configurations for Hitchin's equations
Michael Wolf Sheared Pleated surfaces and Limiting Configurations for Hitchin's equations A recent work by Mazzeo-Swoboda-Weiss-Witt describes a stratum of the frontier of the space of SL(2,C) surface group representations in terms of 'limiting configurations' which solve a degenerate ver
From playlist Maryland Analysis and Geometry Atelier
Limits of cubic differentials and projective structures by David Dumas
ORGANIZERS Siddhartha Gadgil, Krishnendu Gongopadhyay, Subhojoy Gupta and Mahan Mj DATE & TIME 27 November 2017 to 30 November 2017 VENUE Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups int
From playlist Surface Group Representations and Geometric Structures
Sheared Pleated surfaces and Limiting Configurations for Hitchin's equations by Michael Wolf
Surface Group Representations and Geometric Structures DATE: 27 November 2017 to 30 November 2017 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classi
From playlist Surface Group Representations and Geometric Structures
John H. Hubbard: Introduction to Thurston’s theorems
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 20, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM'
From playlist Topology
Find the particular solution with exponential and inverse trig
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
D. Chen - Are affine invariant submanifolds affine
We study the question whether affine invariant submanifolds arising from Teichmueller dynamics are affine varieties in the sense of algebraic geometry.
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
S. Filip - K3 surfaces and Dynamics (Part 1)
K3 surfaces provide a meeting ground for geometry (algebraic, differential), arithmetic, and dynamics. I hope to discuss: - Basic definitions and examples - Geometry (algebraic, differential, etc.) of complex surfaces - Torelli theorems for K3 surfaces - Dynamics on K3s (Cantat, McMullen)
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
The differential calculus for curves (II) | Differential Geometry 8 | NJ Wildberger
In this video we extend Lagrange's approach to the differential calculus to the case of algebraic curves. This means we can study tangent lines, tangent conics and so on to a general curve of the form p(x,y)=0; this includes the situation y=f(x) as a special case. It also allows us to deal
From playlist Differential Geometry