Lectures related to Dirichlet Problem on the Ball

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers the fundamental solutions of the Laplace equation and introduces distributions.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Covers the theory and applications of Green's function in solving differential equations.

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Explores uniqueness results for the Poisson equation and harmonic functions with different boundary conditions.

Covers generalized integrals, convergence criteria, series convergence, and harmonic series in analysis.

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Explores linear similarities and similitudes, demonstrating their properties and applications in geometry.

Covers the general existence result for the Laplace-Dirichlet problem and the properties of the Newtonian potential.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers the properties of harmonic functions and the concept of mollification.

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.

Explores the axiom of separating the plane into two half-planes and the concept of interior points.

Covers the concept of area, axioms, and the area of rectangles.

Explores the concept of universal coating through detailed proofs and examples, emphasizing uniqueness and significance.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers the fundamental operations and constructions in Euclidean geometry, focusing on algebraic interpretations and ruler-and-compass constructions.