Operators on differential forms for Lie transformation groups.
Operators on eigenmaps between spheres
Optics in Croke-Kleiner Spaces
We explore the interior geometry of the CAT(0) spaces , constructed by Croke and Kleiner [Topology 39 (2000)]. In particular, we describe a diffraction effect experienced by the family of geodesic rays that emanate from a basepoint and pass through a certain singular point called a triple point, and we describe the shadow this family casts on the boundary. This diffraction effect is codified in the Transformation Rules stated in Section 3 of this paper. The Transformation Rules have various applications....
Optimal approximations on Riemannian manifolds.
Optimal Boundary Regularity for Minimal Surfaces with a Free Boundary.
Optimal destabilizing vectors in some Gauge theoretical moduli problems
We prove that the well-known Harder-Narsimhan filtration theory for bundles over a complex curve and the theory of optimal destabilizing -parameter subgroups are the same thing when considered in the gauge theoretical framework.Indeed, the classical concepts of the GIT theory are still effective in this context and the Harder-Narasimhan filtration can be viewed as a limit object for the action of the gauge group, in the direction of an optimal destabilizing vector. This vector appears as an extremal...
Optimal inequalities characterising quasi-umbilical submanifolds.
Optimal inequalities for embedded space-times
Optimal regularity for codimension one minimal surfaces with a free boundary.
Optimalité systolique infinitésimale de l’oscillateur harmonique
Nous étudions les aspects infinitésimaux du problème suivant. Soit un hamiltonien de dont la surface d’énergie borde un domaine compact et étoilé de volume identique à celui de la boule unité de . La surface d’énergie contient-elle une orbite périodique du système hamiltoniendont l’action soit au plus ?
Optimization problems on complete Riemannian manifolds
Orbifold adjunction formula and symplectic cobordisms between lens spaces.
Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface (II).
In [6], orbifold G-bundles on a certain class of elliptic fibrations over a smooth complex projective curve X were related to parabolic G-bundles over X. In this continuation of [6] we define and investigate holomorphic connections on an orbifold G-bundle over an elliptic fibration.
Orbihedra of nonpositive curvature
Orbits of families of vector fields on subcartesian spaces
Orbits of complete families of vector fields on a subcartesian space are shown to be smooth manifolds. This allows a description of the structure of the reduced phase space of a Hamiltonian system in terms of the reduced Poisson algebra. Moreover, one can give a global description of smooth geometric structures on a family of manifolds, which form a singular foliation of a subcartesian space, in terms of objects defined on the corresponding family of vector fields. Stratified...
Order of holonomy of a surface with projective connection
Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles
Let be a principal bundle of frames with the structure group . It is shown that the variational problem, defined by -invariant Lagrangian on , can be equivalently studied on the associated space of connections with some compatibility condition, which gives us order reduction of the corresponding Euler-Lagrange equations.
Ordered Manifolds, Invariant Cone Fields, and Semigroups.
Ordnungsgeometrische Limessätze in kompakten Räumen. II. Mitteilung: Punktordnungswerte.
Orientability of higher order Grassmannians