Plateau's Problem for surfaces of constant mean curvature form a global point of view.
Plateau-Stein manifolds
We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.
Plongements lipschitziens dans un espace pentagonal
Pohybové integrály v mechanice vyššího řádu a v teorii polí
Poincaré Lemma for Tangential Cauchy Riemann Complexes.
Poincaré-Cartan forms in higher order variational calculus on fibred manifolds.
The aim of the present work is to present a geometric formulation of higher order variational problems on arbitrary fibred manifolds. The problems of Engineering and Mathematical Physics whose natural formulation requires the use of second order differential invariants are classic, but it has been the recent advances in the theory of integrable non-linear partial differential equations and the consideration in Geometry of invariants of increasingly higher orders that has highlighted the interest...
Poincaré-Hopf index and partial hyperbolicity
We use the theory of partially hyperbolic systems [HPS] in order to find singularities of index for vector fields with isolated zeroes in a -ball. Indeed, we prove that such zeroes exists provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball.
Poincaré-invariant structures in the solution manifold of a nonlinear wave equation.
The solution manifold M of the equation ⎯φ + gφ3 = 0 in Minkowski space is studied from the standpoint of the establishment of differential-geometric structures therein. It is shown that there is an almost Kähler structure globally defined on M that is Poincaré invariant. In the vanishing curvature case g = 0 the structure obtained coincides with the complex Hilbert structure in the solution manifold of the real wave equation. The proofs are based on the transfer of the equation to an ambient universal...
Pointed -surfaces
Let be a Riemann surface. Let be the -dimensional hyperbolic space and let be its ideal boundary. In our context, a Plateau problem is a locally holomorphic mapping . If is a convex immersion, and if is its exterior normal vector field, we define the Gauss lifting, , of by . Let be the Gauss-Minkowski mapping. A solution to the Plateau problem is a convex immersion of constant Gaussian curvature equal to such that the Gauss lifting is complete and . In this paper, we show...
Points critiques dans les problèmes variationnels sans compacité
Pointwise Characterization of Ideals of Differentiable Functions.
Poisson cohomology and canonical homology of Poisson manifolds
In this paper we present recent results concerning the Lichnerowicz-Poisson cohomology and the canonical homology of Poisson manifolds.
Poisson geometry of flat connections for SU(2)-bundles on surfaces.
Poisson kernels of half-spaces in real hyperbolic spaces.
Poisson manifolds, Lie algebroids, modular classes: a survey.
Poisson relation for the scattering kernel and inverse scattering by obstacles
Poisson structures on certain moduli spaces for bundles on a surface
Let be a closed surface, a compact Lie group, with Lie algebra , and a principal -bundle. In earlier work we have shown that the moduli space of central Yang-Mills connections, with reference to appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yields a homeomorphism from onto a certain representation space , in fact a diffeomorphism, with reference to suitable smooth structures and , where denotes the universal central extension of...
Poisson structures on Weil bundles.
Poisson-Nijenhuis structures
Polar quotients and singularities at infinity of polynomials in two complex variables
Using the notion of the maximal polar quotient we characterize the critical values at infinity of polynomials in two complex variables. As an application we give a necessary and sufficient condition for a family of affine plane curves to be equisingular at infinity.