A5009808900- Geometric and Algebraic Topology
- Geometric Analysis and Curvature Flows
- Geometry and complex manifolds
- Homotopy and Cohomology in Algebraic Topology
- Algebraic Geometry and Number Theory
- Advanced Differential Geometry Research
- Computational Geometry and Mesh Generation
- Nonlinear Partial Differential Equations
- Quantum Chromodynamics and Particle Interactions
- High-Energy Particle Collisions Research
- Mathematical Dynamics and Fractals
- Mathematics and Applications
- Topological and Geometric Data Analysis
- Black Holes and Theoretical Physics
- Point processes and geometric inequalities
- History and Theory of Mathematics
- Particle physics theoretical and experimental studies
- Connective tissue disorders research
- Scientific Research and Discoveries
- Nuclear physics research studies
- Distributed and Parallel Computing Systems
- Stability and Controllability of Differential Equations
- Advanced Operator Algebra Research
- Advanced Mathematical Modeling in Engineering
- Orthopedic Surgery and Rehabilitation
Centre National de la Recherche Scientifique
2007-2024
Laboratoire d’Analyse et de Mathématiques Appliquées
2021-2024
Université Paris-Est Créteil
2021-2024
Université Gustave Eiffel
2021-2024
Université de Tours
2014-2020
Laboratoire de Mathématiques et Physique Théorique
2012-2019
Imperial College London
2019
Massachusetts Institute of Technology
2019
Laboratoire de Mathématiques d'Orsay
1991-2019
Virginia Commonwealth University
2019
If M and N are Riemannian manifolds, a harmonic morphism f : → is map which pulls back local functions on to M. an Einstein 4-manifold Riemann surface, John Wood showed that such holomorphic w.r.t. some integrable complex Hermitian structure defined away from the singular points of f. In this paper we extend entire manifold It follows there no non-constant morphisms [Formula: see text] or surface. The proof relies heavily real analyticity whole situation. We conclude by example text].
We study knots in 𝕊 3 obtained by the intersection of a minimal surface ℝ 4 with small 3-sphere centered at branch point. construct new examples knots. In particular we show existence non-fibered that simple are either reversible or fully amphicheiral; this yields an obstruction for given knot to be knot. Properties and invariants these such as algebraic crossing number braid representative Alexander polynomial studied.
We prove that any knot of [Formula: see text] is isotopic to a Fourier type obtained by deformation Lissajous knot.
An isometric immersion $X: \Sigma^n \longrightarrow \mathbb{E}^{n+1}$ is biharmonic if $\Delta^2 X = 0$, i.e. $\Delta H =0$, where $\Delta$ and $H$ are the metric Laplacian mean curvature vector field of $\Sigma^n$ respectively. More generally, biconservative hypersurfaces (BCH) immersions for which only tangential part equation vanishes. We study construct BCH that holonomic, principal directions define an integrable net, we deduce a holonomic hypersurface iff it minimal.
In this paper (S_n) is a sequence of surfaces immersed in 4-manifold which converges to branched surface S_0. Up sign, μ^T_p (resp. μ^N_p) will denote the amount curvature tangent bundles TS_n normal NS_n) concentrates around singular point p S_0 when n goes infinity. By slight abuse notation, we call μ_p^T μ_p^N) normal) Milnor number S_n at p. These numbers are not always well-defined; discuss assumptions under which, if μ^T exists, then μ^N also exists and smaller than -μ^T . When second...
A point in the [Formula: see text]-torus knot text] goes times along a vertical circle while this rotates around axis. In Lissajous-toric text], Lissajous curve (parametrized by Such has natural braid representation which we investigate here. If is ribbon; if text]th power of closes ribbon knot. We give an upper bound for text]-genus spirit genus torus knots; also examples text]’s are trivial knots.
We prove that any knot of $\mathbb{R}^3$ is isotopic to a Fourier type $(1,1,2)$ obtained by deformation Lissajous knot.
A minimal knot is the intersection of a topologically embedded branched disk in $\mathbb{R}^4$ $\mathbb{C}^2 $ with small sphere centered at branch point. When lowest order terms each coordinate component embedding $\mathbb{C}^2$ are enough to determine type, we talk simple knot. Such given by three integers $N < p,q$; denoted $K(N,p,q)$, it can be parametrized cylinder as $e^{iθ}\mapsto (e^{Niθ},\sin qθ,\cos pθ)$. From this expression stems natural representation $K(N,p,q)$ an $N$-braid....
We show that compact orientable Riemannian 4-manifold which is 4/19-pinched homeomorphic to the sphere S 4 or projective space ℂP 2 . Our proof based on estimates of curvature tensor lead an inequality between characteristic numbers.
Nous nous intéressons au volume des variétés riemanniennes dont la métrique est « proche » d'une de courbure constante.En dimension paire, formule Gauss-Bonnet combinée avec une hypothèse pincement (dépendant dimension) donne minoration ce volume.En quelconque, on n'a qu'un résultat infinitésimal : considère d'Einstein et fait varier manière C", variation première scalaire étant signe constant; en déduit alors le du volume.ABSTRACT.-Our purpose is to study thé of those riemannian manifoids...
The Gauss map $g$ of a surface $\Sigma$ in $\mathbb{R}^4$ takes its values the Grassmannian oriented 2-planes $\mathbb{R}^4$: $G^+(2,4)$. We give geometric criteria stability for minimal surfaces terms $g$. show particular that if spherical area $|g(\Sigma)|$ is smaller than $2\pi$ then stable by deformations which fix boundary surface.This answers question Barbosa and Do Carmo $\mathbb{R}^4$.