arXiv research

Note on advancements in nonlinear elliptic equations' regularity theory.

The paper estimates curvature for a specific flow on manifolds.

Develops new strategy for Hessian estimates in Lagrangian mean curvature equation.

We develop a comprehensive study on sharp potential type Riemannian Sobolev inequalities of order 2 by means of a local geometric Sobolev inequality of same kind and suitable De Giorgi-Nash-Moser estimates. In particular we discuss questions like continuous dependence of optimal constants and existence and compactness …

We derive a Harnack inequality for positive solutions of the $f$-heat equation and Gaussian upper and lower bounds for the $f$-heat kernel on complete smooth metric measure spaces $(M, g, e^{-f}dv)$ with Bakry-Émery Ricci curvature bounded below. The lower bound is sharp. The main argument is the De Giorgi-Nash-Moser t…

Alternative proof and extension of curvature estimates for minimal immersions.

Dans les années 1940-1970, Alexandrov et l'"École de Leningrad" ont développé une théorie très riche des surfaces singulières. Il s'agit de surfaces topologiques, munie d'une métrique intrinsèque pour laquelle on peut définir une notion de courbure, qui est une mesure de Radon. Cette classe de surfaces a de bonnes prop…

We show that contact homology distinguishes infinitely many tight contact structures on any orientable, toroidal, irreducible 3-manifold. As a consequence of the contact homology computations, on a very large class of toroidal manifolds, all known examples of universally tight contact structures with nonvanishing torsi…

On décrit ici des relations entre la géométrie globale des variétés de contact closes et celle de certaines variétés symplectiques, à savoir les variétés de Stein compactes. L'origine de ces relations est l'existence de livres ouverts adaptés aux structures de contact. We discuss relations between the global geometry o…

Recursive KalmanNet generalizes well in noisy, out-of-distribution scenarios.

We build examples of properly convex projective manifold $Ω/ Γ$ which have finite volume, are not compact, nor hyperbolic in every dimension $n \geqslant 2$. On the way, we build Zariski-dense discrete subgroups of $\SL_{n+1}(\R)$ which are not lattice, nor Schottky groups. Moreover, the open properly convex set $Ω$ is…

We show that some curvature operators are locally invertible, in some weithted sobolev spaces, near the euclidian metric. (Nous montrons que certains opérateurs affines en la courbure de Ricci sont localement inversibles, dans des espaces de Sobolev à poids, au voisinage de la métrique euclidienne.)

On every compact, orientable, irreducible 3-manifold V which is toroidal or has torus boundary components we construct a contact 1-form whose Reeb vector field R does not have any contractible periodic orbits and is tangent to the boundary. Moreover, if bdry V is nonempty, then the Reeb vector field R is transverse to …

Nous montrons que les équations du repère mobile des surfaces de Bonnet conduisent à une paire de Lax matricielle isomonodromique d'ordre deux pour la sixième équation de Painlevé. We show that the moving frame equations of Bonnet surfaces can be extrapolated to a second order, isomonodromic matrix Lax pair of the sixt…

Two de Rham complexes in diffeology are compared using a factor map.

We describe, in the general setting of closed cone fields, the set of causal functions which can be approximated by smooth Lyapunov. We derive several consequences on causality theory. Dans le contexte général des champs de cones fermés, on décrit l'ensemble des fonctions causales qui peuvent être approchées par des fo…

This paper presents practical methods for portfolio selection in investments.

The so-called risk diversification principle is analyzed, showing that its convenience depends on individual characteristics of the risks involved and the dependence relationship among them. ----- Se analiza el principio de diversificación de riesgos y se demuestra que no siempre resulta mejor que no diversificar, pues…

This article was withdrawn by the author to be incorporated into the paper "Extensão de aplicações na esfera de um espaço vetorial com produto interno" (arXiv:1109.2866).

En nous basant sur les résultats d'Arthur annoncés dans \cite[§30]{Arthur} nous démontrons les conjectures énoncées dans \cite{IMRN,BC,SMF} dans le cas des groupes orthogonaux à l'exclusion des groupes de type ${}^6 - D_4$. En ce qui concerne ces derniers, nous annonçons la démonstration -- encore en préparation - que …

We categorify the coefficients of the Burau representation matrix using elementary geometrical methods. We show the faithfulness of this categorification in the sense that it detects the trivial braid.

Formulas derived for operators on forms in anti-de Sitter spaces.

Despite being very effective in several classification tasks, Dynamic Ensemble Selection (DES) techniques can select classifiers that classify all samples in the region of competence as being from the same class. The Frienemy Indecision REgion DES (FIRE-DES) tackles this problem by pre-selecting classifiers that correc…

Study of de Rham cohomology on non-Hausdorff manifolds.

The theory of Vassiliev invariants deals with many modules of diagrams on which the algebra Lambda defined by Pierre Vogel acts. By specifying a quadratic simple Lie superalgebra, one obtains a character on Lambda. We show the coherence of these characters by building a map of graded algebras beetwen Lambda and a quoti…

Classification of specific pseudo-Riemannian manifolds.

The paper explores de Rham theory for singular spaces and stacks.

De Sitter spacetime can be separated into two parts along two kinds of hypersurfaces and the half-de Sitter spacetimes are covered by the planar and hyperbolic coordinates respectively. Two positive energy theorems were proved previously for certain $¶$-asymptotically de Sitter and $\H$-asymptotically de Sitter initial…

Nous considérons un espace topologique qui est localement isomorphe au quotient de R^k par l'action d'un groupe discret et nous l'appelons quasi-variété de dimension k. Les quasi-variétés généralisent les variétés et les V-variétés et représentent le cadre naturel pour la réduction symplectique par rapport à l'action i…

Proves optimal isoperimetric inequality in de Sitter space.

New Lipschitz de Rham theorem for $L_p$-cohomology.

It is shown that if the Holmes-Thompson volume definition is used, totally geodesic submanifolds of a Finsler space are minimal. The analogous result for the Hausdorff measure is known to be false. ----- Nous montrons que les sous-varietes totalement geodesiques d'une variete de Finsler sont minimales pour le volume de…

Study examines solutions to Jang equation on anti-de Sitter spacetimes.

Constructs many black hole spacetimes in de Sitter space.

Proof of Tholozan's volume formula for anti-de-Sitter 3-manifolds.

Estimates for spacelike hypersurfaces in de Sitter space.

Extended de Rham theorem for manifolds with boundaries.

Link between Teichmüller and anti de Sitter geometry via length functions.

Book provides detailed trading strategies for various asset classes.

On any compact manifold of dimension greater than 6, we prescribe the volume and any finite part of the spectrum Hodge Laplacian acting on $p$-form for $1\leq p<\frac n2$. In particular, we prescribe the multiplicity of the first eigenvalues.

Combines non-Euclidean and de Sitter geometries on the plane.

The paper classifies surfaces with constant curvature in 3D De Sitter and anti De Sitter spaces.

The paper proves formulas and theorems for statistical de Rham Hodge operators on manifolds with boundary.

We prove that direct limits of finite dimensional Lie algebroids and their prolongations can be endowed with structures of convenient spaces.

Study compares survival analysis algorithms with missing data methods.

Study subelliptic heat kernel on octonionic anti-de Sitter space.

The paper studies perturbations of de Rham Hodge operators on manifolds with or without boundaries.

Objective: Patient notes in electronic health records (EHRs) may contain critical information for medical investigations. However, the vast majority of medical investigators can only access de-identified notes, in order to protect the confidentiality of patients. In the United States, the Health Insurance Portability a…