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Lecture
Harmonic Forms: Main Theorem
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Related lectures (30)
Harmonic Forms and Riemann Surfaces
Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.
Differential Forms Integration
Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.
Meromorphic Functions & Differentials
Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.
Fundamental Groups
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Holomorphic Functions: Taylor Series Expansion
Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces, focusing on orientation and orientability.
Open Mapping Theorem
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Local Homeomorphisms and Coverings
Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Distributions and Derivatives
Covers distributions, derivatives, convergence, and continuity criteria in function spaces.
Proper Actions and Quotients
Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.
Hadamard Factorisation
Covers the Hadamard factorisation theorem for entire functions of order at most 1.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.
Curves with Poritsky Property and Liouville Nets
Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.
Complex Analysis: Functions and Their Properties
Covers the fundamentals of complex analysis, focusing on complex functions, their properties, and applications in solving differential equations.
Approximation by Smooth Functions
Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.
Applications of Residue Theorem in Complex Analysis
Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.
Preliminaries in Measure Theory
Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.
Cauchy Equations and Integral Decomposition
Covers the application of Cauchy equations and integral decomposition, addressing questions related to holomorphic functions and Jacobian matrices.
Linear Independence: The Wronskian Concept
Explains the Wronskian and its role in determining linear independence of solutions to differential equations.
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