The Serre Problem on Riemann Surfaces.
The Serre problem with Reinhardt fibers
The Serre problem is solved for fiber bundles whose fibers are two-dimensional pseudoconvex hyperbolic Reinhardt domains.
The set of points at which a polynomial map is not proper
We describe the set of points over which a dominant polynomial map is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by .
The Shafarevich-Tate Conjecture for Pencils of Elliptic Curves on K3 Surfaces.
The Siciak-Zahariuta extremal function as the envelope of disc functionals
We establish disc formulas for the Siciak-Zahariuta extremal function of an arbitrary open subset of complex affine space. This function is also known as the pluricomplex Green function with logarithmic growth or a logarithmic pole at infinity. We extend Lempert's formula for this function from the convex case to the connected case.
The Signature of Milnor Fibres and Duality Theorem for Strongly Pseudoconvex Manifolds.
The Signature of Smoothings of Complex Surface Singularities.
The singularities of Yang-Mills connections for bundles on a surface.
The Sobolev inequality on the Heisenberg group and the Yamabe problem on CR manifolds (d'après travaux avec J. M. Lee)
The Soliton-Ricci Flow with variable volume forms
We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previouswork.We still call this new flow, the Soliton-Ricci flow. It corresponds to a forward Ricci type flow up to a gauge transformation. This gauge is generated by the gradient of the density of the volumes. The new Soliton-Ricci flow exist for all times. It represents the gradient flow of...
The Solution of the ...-Neumann Problem in a Strictly Pseudoconvex Siegel Domain.
The space of holomorphic functions on bounded symmetric domains
The space of quasisymmetric mappings.
The space of Surface group representations.
The stack of microlocal perverse sheaves
In this paper we construct the abelian stack of microlocal perverse sheaves on the projective cotangent bundle of a complex manifold. Following ideas of Andronikof we first consider microlocal perverse sheaves at a point using classical tools from microlocal sheaf theory. Then we will use Kashiwara-Schapira’s theory of analytic ind-sheaves to globalize our construction. This presentation allows us to formulate explicitly a global microlocal Riemann-Hilbert correspondence.
The Strong Rigidity of Locally Symmetric Complex Manifolds of Rank One and Finite Volume.
The structure of polynomial ideals in the algebra of entire functions
The structure of proper rigid groups.
The super complex Frobenius theorem
We formulate and prove a super analogue of the complex Frobenius theorem of Nirenberg.
The supports of higher bifurcation currents
Let be a holomorphic family of rational mappings of degree on , with marked critical points . To this data is associated a closed positive current of bidegree on , aiming to describe the simultaneous bifurcations of the marked critical points. In this note we show that the support of this current is accumulated by parameters at which eventually fall on repelling cycles. Together with results of Buff, Epstein and Gauthier, this leads to a complete characterization of .