58 citations · 154 across the 9 of their papers we have counts for
10 papers
Dynamical mechanisms for Kaluza-Klein theories
Frédéric Hélein
We present variational formulations of gauge theories and Einstein--Yang-Mills equations in the spirit of Kaluza-Klein theories. For gaugetheories, only a topological fibration is…
A remark on compact H-surfaces into R^3
Yuxin Ge, Frédéric Hélein
Using the functional associated with the optimal Wente inequality for pairs of functions on 2-dimensional domains, we show the existence of solutions to the H-system on an annulus…
Continuity of the fundamental operations on distributions having a specified wave front set (with a counter example by Semyon Alesker)
Christian Brouder, Nguyen Viet Dang, Frédéric Hélein
The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front set satisfies some conditions. Thus, it is natural to invest…
Multisymplectic formulation of Yang--Mills equations and Ehresmann connections
Frédéric Hélein
We present a multisymplectic formulation of the Yang--Mills equations. The connections are represented by normalized equivariant 1-forms on the total space of a principal bundle, w…
A smooth introduction to the wavefront set
Christian Brouder, Nguyen Viet Dang, Frédéric Hélein
The wavefront set provides a precise description of the singularities of a distribution. Because of its ability to control the product of distributions, the wavefront set was a key…
First integrals for nonlinear dispersive equations
Frédéric Hélein
Given a solution of a semilinear dispersive partial differential equation with a real analytic nonlinearity, we relate its Cauchy data at two different times by nonlinear represent…
A note on some overdetermined elliptic problem
Frédéric Hélein, Laurent Hauswirth, Frank Pacard
We define the notion of an exceptional manifold to be a flat Riemannian manifold with boundary which supports a positive harmonic function satisfying simultaneously a zero Dirichle…
First integrals for non linear hyperbolic equations
Dikanaina Harrivel, Fréderic Hélein
Given a solution of a nonlinear wave equation on the flat space-time (with a real analytic nonlinearity), we relate its Cauchy data at two different times by nonlinear representati…
Hamiltonian stationary tori in the complex projective plane
Frédéric Hélein, Pascal Romon
We analyze here Hamiltonian stationary surfaces in the complex projective plane as (local) solutions to an integrable system, formulated as a zero curvature on a loop group. As an…
Finite dimesional Hamiltonian formalism for gauge and field theories
Frédéric Hélein, Joseph Kouneiher
We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} Hamiltonian formulation, where we put forward the role…