Related papers: Higher-order Riemannian spline interpolation probl…
Particle flow processing is widely employed across various industrial applications and technologies. Due to the complex interactions between particles and fluids, designing effective devices for particle flow processing is challenging. In…
This paper is devoted to the investigation of gradient flows in asymmetric metric spaces (for example, irreversible Finsler manifolds and Minkowski normed spaces) by means of discrete approximation. We study basic properties of curves and…
This paper deals with Hermite osculatory interpolating splines. For a partition of a real interval endowed with a refinement consisting in dividing each subinterval into two small subintervals, we consider a space of smooth splines with…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…
This paper is devoted to rigidity results for some elliptic PDEs and related interpolation inequalities of Sobolev type on smooth compact connected Riemannian manifolds without boundaries. Rigidity means that the PDE has no other solution…
This paper studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…
This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.
We are interested in the challenging problem of modelling densities on Riemannian manifolds with a known symmetry group using normalising flows. This has many potential applications in physical sciences such as molecular dynamics and…
Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…
Research on smooth vector graphics is separated into two independent research threads: one on interpolation-based gradient meshes and the other on diffusion-based curve formulations. With this paper, we propose a mathematical formulation…
We describe some new univariate spline quasi-interpolants on uniform partitions of bounded intervals. Then we give some applications to numerical analysis: integration, differentiation and approximation of zeros.
The isometric embedding problem for Riemannian manifolds, which connects intrinsic and extrinsic geometry, is a central question in differential geometry with deep theoretical significance and wide-ranging applications. Despite extensive…
We obtain height, gradient, and curvature a priori estimates for a modified mean curvature flow in Riemannian manifolds endowed with a Killing vector field. As a consequence, we prove the existence of smooth, entire, longtime solutions for…
We generalize the technique of [Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains, SIAM J. Sci. Comput. 34, pp. A497--A519 (2012)] to elliptic problems with mixed boundary conditions and elliptic…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
We introduce a new parabolic flow deforming any Riemannian metric on a spin manifold by following a constrained gradient flow of the total scalar curvature. This flow is built out of the well-known Dirac-Einstein functional. We prove local…
We introduce a general framework for training flow matching models on Riemannian symmetric spaces, a large class of manifolds that includes the sphere, hyperbolic space and Grassmannians. We exploit their algebraic structure to reformulate…
Using a residuum approach, we provide a complete description of the space of the rational spatial curves of given tangent directions. The rational Pythagorean hodograph curves are obtained as a special case when the norm of the direction…
In this letter we study variational obstacle avoidance problems on complete Riemannian manifolds. The problem consists of minimizing an energy functional depending on the velocity, covariant acceleration and a repulsive potential function…