Introduces Manopt, a toolbox for optimization on smooth manifolds with a Riemannian structure, covering cost functions, different types of manifolds, and optimization principles.
Explores transporters as a practical alternative to parallel transport, discussing minimal requirements, examples with matrices, pragmatic choices, and optimization algorithms.
Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.
Explores geodesic convexity and its extension to optimization on manifolds, emphasizing the preservation of the key fact that local minima imply global minima.