Lipschitz spaces of holomorphic and pluriharmonic functions on bounded symmetric domains in (N>1)
LVM and LVMB manifolds are a large family of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a natural action of a real torus and the quotient of this action is a polytope. This quotient allows us to relate closely LVM manifolds to the moment-angle manifolds studied by Buchstaber and Panov. Our aim is to generalize the polytope associated to a LVM manifold to the LVMB case and study the properties of this generalization....
We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space for every dimension and every degree . Precisely, we construct a foliation which is induced by a homogeneous vector field of degree , has a finite singular set and all the regular leaves are dense in the whole of . Moreover, satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if is conjugate to another holomorphic foliation...
Besov spaces of holomorphic functions in tubes over cones have been recently defined by Békollé et al. In this paper we show that Besov p-seminorms are invariant under conformal transformations of the domain when n/r is an integer, at least in the range 2-r/n < p ≤ ∞.
We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective holonomy representations whose topological invariance was conjectured in the eighties by Cerveau and Sad and is proved here under mild hypotheses.
We give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups , , and .