We show that a bounded pseudoconvex domain D ⊂ ℂⁿ is hyperconvex if its boundary ∂D can be written locally as a complex continuous family of log-Lipschitz curves. We also prove that the graph of a holomorphic motion of a bounded regular domain Ω ⊂ ℂ is hyperconvex provided every component of ∂Ω contains at least two points. Furthermore, we show that hyperconvexity is a Hölder-homeomorphic invariant for planar domains.
In this paper we use Nachbin’s holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables
Applying the “exact WKB method” (cf. Delabaere-Dillinger-Pham) to the stationary one-dimensional Schrödinger equation with polynomial potential, one is led to a multivalued complex action-integral function. This function is a (hyper)elliptic integral; the sheet structure of its Riemann surface above the plane of its values has interesting properties: the projection of its branch-points is in general a dense subset of the plane, and there is a group of symmetries acting on the surface. The distribution...
Let M be a hyperkähler manifold, and F a reflexive sheaf on M. Assume that F (away from its singularities) admits a connection ▿ with a curvature Θ which is invariant under the standard SU(2)-action on 2-forms. If Θ is square-integrable, such sheaf is called hyperholomorphic. Hyperholomorphic sheaves were studied at great length in [21]. Such sheaves are stable and their singular sets are hyperkähler subvarieties in M. In the present paper, we study sheaves admitting a connection with SU(2)-invariant...
There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank local systems on the complement of the arrangement to gain information on the homology of the other three spaces, and on the monodromy operators of the various fibrations.
We prove that the exceptional complex Lie group has a transitive action on the hyperplane section of the complex Cayley plane . Although the result itself is not new, our proof is elementary and constructive. We use an explicit realization of the vector and spin actions of . Moreover, we identify the stabilizer of the -action as a parabolic subgroup (with Levi factor ) of the complex Lie group . In the real case we obtain an analogous realization of .
Soit un germe en de 1-forme différentielle holomorphe, satisfaisant la condition d’intégrabilité et non dicritique, i.e. sur toute surface non intégrale de , on ne peut tracer, au voisinage de 0, qu’un nombre fini de germes de courbes analytiques , intégrales de , avec . Alors possède un germe d’hypersurface analytique intégrale.