arXiv research

This work tackles force control for contact-rich manipulation tasks with rigid robots using RL.

Paper provides closed-form time derivatives for rigid body systems.

The paper investigates quantitative rigidity using Colding's monotonicity formulas for Ricci curvature.

We prove explicit upper and lower bounds for the torsional rigidity of extrinsic domains of submanifolds P^m with controlled radial mean curvature in ambient Riemannian manifolds N^n with a pole p and with sectional curvatures bounded from above and from below, respectively. These bounds are given in terms of the torsi…

Researchers prove rigidity of first conformal Steklov eigenvalue on specific shapes.

Paper proves rigidity for Ricci solitons with specific conditions.

New Gromov-Wasserstein metric controls rigidity and incorporates prior knowledge.

New boundary and point constraints for controlling conformal surfaces.

Model learns Lagrangian dynamics from images for better prediction and control.

A new method for non-rigid point set registration reduces computational complexity.

By means of a space-time Wasserstein control, we show the monotonicity of the W-entropy functional in time along heat flows on possibly singular metric measure spaces with non-negative Ricci curvature and a finite upper bound of dimension in an appropriate sense. The associated rigidity result on the rate of dissipatio…

The paper extends rigidity results for $λ$-self-expanders to hyperplanes, spheres, and cylinders.

The paper proves surfaces close to spheres under specific conditions.

We find Weitzenböck formula for the Fueter-Dirac operator which controls the infinitesimal deformations of an associative submanifold in a $7$--manifold with a $G_2$--structure. We establish a vanishing theorem to conclude rigidity under some positivity assumptions on curvature, which are particularly mild in the nearl…

We obtain a bound for the area of a capillary $H-$surface in a three-manifold with umbilic boundary and controlled sectional curvature. We then analyze the geometry when this area bound is realized, and obtain rigidity theorems. As a side product, we obtain existence of totally geodesic embedded surfaces in hyperbolic …

Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual approach, which consists to enrich a plane field, as this is often practised in cont…

Real-life control tasks involve matters of various substances---rigid or soft bodies, liquid, gas---each with distinct physical behaviors. This poses challenges to traditional rigid-body physics engines. Particle-based simulators have been developed to model the dynamics of these complex scenes; however, relying on app…

In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on Lie groups, deriving a discrete version of the second-order Euler-Lagrange equatio…

The study proves topological rigidity for certain geometric shapes using Poincaré inequalities.

Sharp estimate shows maps with small energy defect are close to rational maps.

We propose a sliding surface for systems on the Lie group $SO(3)\times \mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable equilibrium. The sliding surface is used to design a sliding-mode controller for t…

Paper proves rigidity theorems for AE Q-singular spaces.

New equations reveal moduli space rigidity in geometric deformations.

Second part of Q-curvature research focusing on volume comparison.

Study of motion control systems on Lie groups with specific geometric constraints.

Classifies positive solutions to critical p-Laplace equation.

The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects generalizing Lie algebroids. This formulation of the PMP yields, in particular, a scheme comprising reductions of optimal control problems simil…

Optimizes angular velocity transfers for rigid bodies under deadline constraints.

Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one has explicit control over the curvature tensor, we completely classify such foliations by studying the infinitesimal model associated to the canonical connection. …

The paper establishes curvature inequalities and rigidity results for surfaces in Riemannian and Lorentzian geometry.

The paper establishes curvature inequalities and rigidity results for CMC and STCMC surfaces in Riemannian and Lorentzian geometry.

Study positive entropy actions by higher-rank lattices, proving rigidity and conjugacy results.

The Positive Mass Theorem for special singular initial data.

Study on manifolds with density using modified Hessians for curvature comparison.

We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several fundamental properties of the deformation cohomology including Morita invariance…

We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens in the classical case, we show that the Lipschitz constant of the nonlocal mean curvature of such a boundary controls its $C^2$-distance fro…

Study proves topological properties of isoperimetric sets in specific spaces.

There has been much recent interest into those properties of a 3-manifold determined by the profinite completion of its fundamental group. In this paper we give readily computable criteria specifying precisely when two orientable graph manifold groups have isomorphic profinite completions. Our results also distinguish …

We give an explicit estimate of the distance of a closed, connected, oriented and immersed hypersurface of a space form to a geodesic sphere and show that the spherical closeness can be controlled by a power of an integral norm of the traceless second fundamental form, whenever the latter is sufficiently small. Further…

Unified theory of $θ$-expectations derived from chaotic dynamics.

This thesis applies RL to market making in China's commodity market.

Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few uncertain variables or require large amounts of simulation data. In this paper, we…

The paper examines properties and rigidity of self-expanders in Euclidean space.

The study proves that sets with constant nonlocal curvature are composed of equal balls under certain conditions.

The paper studies symmetry reduction and optimal control on Riemannian manifolds.

GWIL uses Gromov-Wasserstein distance to align expert and imitation agent states.

Study automorphism groups of Artin groups, proving rigidity and classification results.

Spinors prove rigidity for polyhedral spacetime data.