As data is a predominant resource in applications, Riemannian geometry is a natural
framework to model and unify complex nonlinear sources of data. However, the …

On the space of probability densities, we extend the Wasserstein geodesics to the case of
higher-order interpolation such as cubic spline interpolation. After presenting the natural …

In this paper, we describe a geometric setting for higher-order Lagrangian problems on Lie
groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an …

Numerical methods that preserve geometric invariants of the system, such as energy,
momentum or the symplectic form, are called geometric integrators. In this paper we present …

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In this paper we investigate the existence and uniqueness of Riemannian cubics under
boundary conditions on position and velocity. We restrict the study to cubics close to …

This paper presents a derivation of the parallel transport equation expressed in the Lie
algebra of a Lie group endowed with a left-invariant metric. The use of this equation is …

This paper develops a method for higher order parametric regression on diffeomorphisms
for image regression. We present a principled way to define curves with nonzero …

Discrete variational methods have shown an excellent performance in numerical simulations
of different mechanical systems. In this paper, we introduce an iterative method for discrete …

This paper presents symmetry reduction for material stochastic Lagrangian systems with
advected quantities whose configuration space is a Lie group. Such variational principles …