arXiv research

Study on homeomorphism groups of manifolds using set theory.

Proves existence of sentences to identify homeomorphic manifolds.

We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations). Given two curves, the distance between them is defined as the infimum of an energy …

The paper studies Riemannian four-manifolds and their twistor spaces using a moving frame approach.

Locally approximating groups of homeomorphisms reveal manifold properties.

We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties: not on…

We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are ``convex co-compact'' in a natural sense. We prove an infinitesimal rigidity statement when the angle around the singular lines is less than $π$: any first-order deformation changes either one of those angles or the conformal …

Given a singular Schubert variety Z in a compact Hermitian symmetric space it is a longstanding question to determine when Z is homologous to a smooth variety Y. We identify those Schubert varieties for which there exist first-order obstructions to the existence of Y. This extends (independent) work of M. Walters, R. B…

Let (M, π ) be a Poisson manifold. A Poisson submanifold $P \in M$ gives rise to an algebroid $AP \rightarrow P$, to which we associate certain chomology groups which control formal deformations of π around P . Assuming that these groups vanish, we prove that π is formally rigid around P , i.e. any other Poisson struct…

We describe the first-order variations of the angles of Euclidean, spherical or hyperbolic polygons under infinitesimal deformations such that the lengths of the edges do not change. Using this description, we introduce a vector-valued quadratic invariant $b$ on the space of those isometric deformations which, for conv…

The study shows how geometric Weyl bulk-density exponent rigidifies spectral encodings in O-regularly varying classes.

This paper presents a geometric-variational approach to continuous and discrete {\it second-order} field theories following the methodology of \cite{MPS}. Staying entirely in the Lagrangian framework and letting $Y$ denote the configuration fiber bundle, we show that both the multisymplectic structure on $J^3Y$ as well…

Examines how first-order differential operators can be equivalently transformed.

New geometric quantities help classify manifolds and relate to entropy.

New vector fields integrate first-order ODEs.

Study first-order locally convex Lie algebroids in Bastiani calculus.

A new method solves complex constrained minimax problems.

A guide for solving first-order elliptic boundary value problems.

First-order ODEs linked to flat surfaces, leading to integrability.

Extends a theorem for first-order elliptic operators on manifolds.

Two classes of methods have been proposed for escaping from saddle points with one using the second-order information carried by the Hessian and the other adding the noise into the first-order information. The existing analysis for algorithms using noise in the first-order information is quite involved and hides the es…

For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up to smooth orbital equivalence. Besides the well known singularities of generic vector fields on the plane and the singularit…

We consider first order expansions of convex penalized estimators in high-dimensional regression problems with random designs. Our setting includes linear regression and logistic regression as special cases. For a given penalty function $h$ and the corresponding penalized estimator $\hatβ$, we construct a quantity $η$,…

Efficient algorithm for contextual bandits with first-order guarantees.

Extends first-order flexes of surfaces to second-order flexes.

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

Spinors prove rigidity for polyhedral spacetime data.

Optimal first-order methods are shown to be fundamental limits in functional estimation.

Survey on rigidity and almost rigidity of Green functions in non-negative Ricci curvature spaces.

In this article, we discuss the local rigidity of Clifford-Klein forms of homogeneous spaces of 1-connected completely solvable Lie groups. In fact, we introduce a splitting of the local rigidity: vertical rigidity and horizontal rigidity. By using this splitting, we refine some existing results about the local rigidit…

First order discretizations of Langevin diffusion can achieve better generalization error with additional smoothness assumptions.

The aim of this paper is fourfold. Firstly, we introduce and study the f-ultra-harmonic maps. Secondly, we recall the geometric dynamics generated by a first order normal PDE system and we give original results regarding the geometric dynamics generated by other first order PDE systems. Thirdly, we determine the Gauss …

CEFOL uses deep learning for dynamic programming with recursive utility.

The properties of the Riemann extensions of nonriemannian spaces defined by the first order systems of differential equations are considered.

Study shows critical width for rigidity of equatorial zones on spheres.

Projective structures are mostly rigid at the boundary but some are not.

The paper explores conditions for topological rigidity in quotients of the Davis complex.

Non-rigidity of hyperbolic manifold under scalar curvature constraints.

We analyze sub-Riemannian and lightlike metrics from the point of view of their rigidity as geometric structures. Following Cartan's and Gromov's formal definitions, they are never rigid, yet, in generic cases, they naturally give rise to rigid geometric structures!?

Study scattering rigidity on stationary manifolds using geodesics.

Study rigid classes on hyperkahler manifolds, showing general ones are rigid.

We propose a unified computational framework for the problem of deformation and rigidity of submanifolds in a homogeneous space under geometric constraint. A notion of 1-rigidity of a submanifold under admissible deformations is introduced. It measures how a deformation deviates from a one parameter family of motions u…

Entropy rigidity proven for 3D and higher convex projective manifolds.

In this paper, we discuss a rigidity property for holomorphic disks in Teichmüller space. In fact, we give a refinement of Tanigawa's rigidity theorem. We will also treat the rigidity property of holomorphic disks for complex manifolds. We observe the rigidity property is valid for bounded strictly pseudoconvex domains…

New algorithm reduces online decision-making regret with efficient LP re-solving and parallel first-order method.

A geometric multisymplectic formulation of the classical BRST symmetry of constrained first-order classical field theories is described. To effect this we introduce graded analogues of the bundles and manifolds of the multisymplectic formulation of first-order field theories. The Lagrange-d'Alembert formalism is also d…

The flip graph and arc complex of a surface are shown to have finite rigidity.

Every noncompact surface has a 3-rigid triangulation.