Publications related to L-2-cohomology and complete Hamiltonian manifolds

Some applications of symmetries in differential geometry and dynamical systems

This thesis deals with applications of Lie symmetries in differential geometry and dynamical systems. The first chapter of the thesis studies the singular reduction of symmetries of cosphere bundles, the conservation properties of contact systems and their ...

EPFL2007

Sobolev inequalities for differential forms and $L_{q,p}$-cohomology

Marc Troyanov

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold

(M,g)

and the

L_{q,p}

-cohomology of that manifold. The

L_{q,p}

-cohomology of

(M,g)

is defined to be the quotient of the space of closed differential ...

2006

Solving the $p$-Laplacian on manifolds

Marc Troyanov

We prove in this paper that the equation

\Delta _{p}u+h=0

on a

p

- hyperbolic manifold

M

has a solution with

p

-integrable gradient for any bounded measurable function

h : M \to \mathbb R

with compact support. ...

2000

Solving the p-Laplacian on manifolds

Marc Troyanov

We prove in this paper that the equation

Delta _{p}u+h=0

on a p-hyperbolic manifold M has a solution with p-integrable gradient for any bounded measurable function h : M -> R with compact support. ...

2000

Parabolicity of manifolds

Marc Troyanov

This Paper is an introduction to the study of an invariant of Riemannian manifolds related to the non-linear potential theory of the p-Laplacian and which is called its parabolic or hyperbolic type. One of our main focus is the relationship between the asy ...

1999

L-2-cohomology and complete Hamiltonian manifolds

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Some applications of symmetries in differential geometry and dynamical systems

Sobolev inequalities for differential forms and $L_{q,p}$-cohomology

Solving the $p$-Laplacian on manifolds

Solving the p-Laplacian on manifolds

Parabolicity of manifolds

Parabolicity of manifolds

Some applications of symmetries in differential geometry and dynamical systems

Sobolev inequalities for differential forms and $L_{q,p}$-cohomology

Solving the $p$-Laplacian on manifolds

Solving the p-Laplacian on manifolds