A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Solves Plateau problem for surfaces in pinched curvature manifolds.
The paper is focused on the existence problem of attractors for foliations. Since the existence of an attractor is a transversal property of the foliation, it is natural to consider foliations admitting transversal geometric structures. As transversal structures are chosen Cartan geometries due to their universality. T…
Study on geodesics in Cartan group sub-Riemannian problem, proving conjugate time relation to Maxwell time.
New method solves Cartan's problem for Lie algebroids and groupoids.
Paper solves equivalence problems for fifth-order differential operators using Cartan's method.
An intrinsic description of the Hamilton-Cartan formalism for first-order Berezinian variational problems determined by a submersion of supermanifolds is given. This is achieved by studying the associated higher-order graded variational problem through the Poincaré-Cartan form. Noether theorem and examples from superfi…
We apply the language of the groupoid approach to Lie pseudo-groups, and the classical Cartan-Kuranishi theorem, to prove that Cartan's equivalence method terminates at involution (or at complete reduction) for constant type problems.
Survey on minimal surface equation on Cartan-Hadamard manifolds.
Study extends isometric immersions using submanifolds.
Classifies multiply-transitive (2,3,5)-distributions using modern Cartan geometry.
The study provides criteria for solving the Dirichlet problem at infinity on Cartan-Hadamard surfaces.
Researchers find optimal paths on a specific geometric group.
Elie Cartan's general equivalence problem is recast in the language of Lie algebroids. The resulting formalism, being coordinate and model-free, allows for a full geometric interpretation of Cartan's method of equivalence via reduction and prolongation. We show how to construct certain normal forms (Cartan algebroids) …
Weyl and Cartan proposed different but related ways to handle infinitesimal geometry in the early 1920s.
Sharp spectral gap estimates for higher-order operators on hyperbolic spaces.
New method solves problem using global Cartan decompositions.
The Cartan-Kähler theorem is extended to Lie algebroids.
Closed surfaces minimize total curvature in curved spaces.
This article is dedicated to solve the equivalence problem for two third order differential operators on the line under general fiber--preserving transformation using the Cartan method of equivalence. We will do three versions of the equivalence problems: first via the direct equivalence problem, second equivalence pro…
In this paper, we first provide an updated survey of the geometry of complex Cartan spaces. New characterizations for some particular classes of complex Cartan spaces are pointed out, e.g. Landsberg-Cartan, strongly Berwald-Cartan and others. We introduce the Cartan-Randers spaces which offer examples of Berwald-Cartan…
Formula for comparing total curvature in curved spaces, with applications to isoperimetric problems.
After recalling the Dirichlet problem at infinity on a Cartan-Hadamard manifold, we discuss what is known and the difference between the two-dimensional and higher-dimensional cases. Turning our attention to the two-dimensional case, we prove that the Dirichlet problem at infinity on a two-dimensional Cartan-Hadamard m…
Nonexistence of radial optimal functions on certain Cartan-Hadamard manifolds.
We study the equivalence problem for -dimensional CR-manifolds of CR-dimension and codimension which are referred to as Engel CR-manifolds. We construct a canonical Cartan connection on such CR-manifolds through Cartan equivalence's method. In particular, we give the explicit expression of biholomorphic …
The aim of the paper is to demonstrate the superiority of Cartan's method over direct methods based on differential elimination for handling otherwise intractable equivalence problems. In this sens, using our implementation of Cartan's method, we establish two new equivalence results. Weestablish when a system of secon…
Develops infinite-dimensional Kempf-Ness theory for complexification-free groups.
The paper extends Cartan development to infinite dimensional Lie groups.
Motivated by our attempt to recast Cartan's work on Lie pseudogroups in a more global and modern language, we are brought back to the question of understanding the linearization of multiplicative forms on groupoids and the corresponding integrability problem. From this point of view, the novelty of this paper is that w…
Study finds solitons on curved spaces with varying behavior.
Following the Cartans's original method of equivalence supported by methods of parabolic geometry, we provide a complete solution for the equivalence problem of quaternionic contact structures, that is, the problem of finding a complete system of differential invariants for two quaternionic contact manifolds to be loca…
We study the asymptotic Dirichlet problem for A-harmonic equations and for the minimal graph equation on a Cartan-Hadamard manifold M whose sectional curvatures are bounded from below and above by certain functions depending on the distance to a fixed point in M. We are, in particular, interested in finding optimal (or…
We consider the local equivalence problem for the class of linear second order hyperbolic equations in two independent variables under an action of the pseudo-group of contact transformations. E. Cartan's method is used for finding the Maurer - Cartan forms for symmetry groups of equations from the class and computing …
Study investigates non-existence of bounded solutions on curved spaces.
We define what we call morphisms of Cartan connections. We generalize the main theorems on Cartan connections to theorems on morphisms. Many of the known constructions involving Cartan connections turn out to be examples of morphisms. We prove some basic results concerning completeness of Cartan connections. We provide…
The extension functors between categories of Cartan geometries can be used to define different categories of Cartan geometries with additional morphisms. The Cartan geometries modeled on skeletons can be used for the description of such categories of Cartan geometries and therefore we develop the theory of Cartan geome…
New perspective on Cartan geometries using multiplicative forms.
Introduces logarithmic Cartan geometry on complex manifolds with singularities.
In 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions on a 5-dimensional manifold. We solve the analogous problems for rank 2 distributions on an n-dimensional manifold for arbitrary n greater than 5. Our method is a kind of symplectification…
In this review article we discuss four recent methods for computing Maurer-Cartan structure equations of symmetry groups of differential equations. Examples include solution of the contact equivalence problem for linear hyperbolic equations and finding a contact transformation between the generalized Hunter-Saxton equa…
Extends Polydisk Theorem to Cartan-Hartogs domains.
Study natural foliations in cotangent bundles of Cartan spaces.
The paper explores symplectic geometry of Cartan-Hartogs domains.
In 1931 Elie Cartan constructed a geometry which was rarely considered. Cartan proposed a way to define an infinitesimal metric starting from a variational problem on hypersurfaces in an -dimensional manifold . This distance depends not only of the point $\textsc{m}\in\mathcal{M}$ but on the orient…
Constructs Chern-Weil classes for Cartan geometries.
The paper examines torsions in Minkowskian product of Finsler metrics.
Explains Cartan geometries for graduate students.
We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold.
The paper explores the connection between 3d gravity and Chern-Simons theory using affine group connections.