Riemannian distance, geodesically convex sets

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Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Explores linear convergence with the Polyak-Łojasiewicz condition on a Riemannian manifold.

Explores Riemannian metrics on manifolds and the concept of Riemannian submanifolds in Euclidean spaces.

Explains Riemannian submanifolds, metrics, and gradients computation on manifolds.

Covers the definition and computation of Riemannian Hessians on manifolds.

Covers Newton's method on Riemannian manifolds, focusing on second-order optimality conditions and quadratic convergence.

Explores stereographic projection and metric tensors on hyperbolic planes, emphasizing isometry and conforming models.

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

Explores matrix-based approaches for computing the Newton step on a Riemannian manifold.

Explores Taylor expansions and retractions on Riemannian manifolds, emphasizing second-order approximations and covariant derivatives.

Covers the convergence theorem of Riemannian Gradient Descent and the line search method.

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