Optimal Transport: Convexity and Inequalities

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Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

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

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores convex sets, Minkowski-Weyl theorem, and Separation theorem in convex analysis.

Covers the concept of convex functions and their applications in optimization problems.

Covers the proof of the Jordan Curve Theorem and the properties of embedded spheres.

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