Riemannian distance, geodesically convex sets

Related lectures (40)

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.

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

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

Covers geodesically convex optimization on Riemannian manifolds, exploring convexity properties and minimization relationships.

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.

Explores symmetries, Riemannian connection, vector fields, and Lie bracket in geometry.

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

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

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

Explores surfaces with constant curvature, emphasizing the significance of minimal oriented radius and the properties of pseudo-spheres.

Explores approximating curves in space and preparing for an upcoming exam.

Introduces d-dimensional charts on manifolds and the concept of an atlas.

Discusses geometric principles in architecture, focusing on hyperboloids and paraboloids and their applications in design and structural engineering.

Explores the Second Separation Theorem for closed convex sets and the concept of supporting hyperplanes.

Covers curves in R^2, regular surfaces in R^3, and geometric properties of edges.

Covers Banach and Hilbert spaces, separability, norm, continuity, and functional analysis.

Explores the intersection multiplicity of curves and the absence of common tangent lines.

Page 2 of 2