A Simplification and Extension of Fefferman's Theorem on Biholomorphic Mappings.
A solution to the delta operator-problem for holomorphic (0,q)-forms, q ≥ 1, on a complex normed space.
A viscosity approach to degenerate complex Monge-Ampère equations
This is the content of the lectures given by the author at the winter school KAWA3 held at the University of Barcelona in 2012 from January 30 to February 3. The main goal was to give an account of viscosity techniques and to apply them to degenerate Complex Monge-Ampère equations.We will survey the main techniques used in the viscosity approach and show how to adapt them to degenerate complex Monge-Ampère equations. The heart of the matter in this approach is the “Comparison Principle" which allows...
About the Calabi problem: a finite-dimensional approach
Let us consider a projective manifold and a smooth volume form on . We define the gradient flow associated to the problem of -balanced metrics in the quantum formalism, the -balancing flow. At the limit of the quantization, we prove that (see Theorem 1) the -balancing flow converges towards a natural flow in Kähler geometry, the -Kähler flow. We also prove the long time existence of the -Kähler flow and its convergence towards Yau’s solution to the Calabi conjecture of prescribing the...
An eigenvalue problem for the complex Monge-Ampère operator in pseudoconvex domains
An energy estimate for the complex Monge-Ampère operator
We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.
An example of the Heisenberg group
Analycity of CR Equivalences Between Some Real Hypersurfaces in ...n with Degenerate Levi Forms.
Analyticité globale pour sur certaines hypersurfaces compactes de
Analyticité semi-globale pour le -Neumann dans des domaines pseudoconvexes
Approximation de fonctions holomorphes d'un nombre infini de variables
Soit un espace de Banach complexe, et notons la boule de rayon centrée en . On considère le problème d’approximation suivant: étant donnés , et une fonction holomorphe dans , existe-t-il toujours une fonction , holomorphe dans , telle que sur ? On démontre que c’est bien le cas si est l’espace des suites sommables.
Approximation in .
Approximation of Plurisubharmonic Functions and the Dirichlet Problem for the Complex Monge-Ampère Operator.
Athe ...-Neumann Operator on the Unit Ball in Cn.
Automorphisms of certain Stein mainfolds.
Banach space properties of strongly tight uniform algebras
We use the work of J. Bourgain to show that some uniform algebras of analytic functions have certain Banach space properties. If X is a Banach space, we say X is strongif X and X* have the Dunford-Pettis property, X has the Pełczyński property, and X* is weakly sequentially complete. Bourgain has shown that the ball-algebras and the polydisk-algebras are strong Banach spaces. Using Bourgain’s methods, Cima and Timoney have shown that if K is a compact planar set and A is R(K) or A(K), then A and...
Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves
We show that in the class of compact, piecewise curves K in , the semialgebraic curves are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for the derivatives of (the traces of) polynomials on K.
Beschränkte Integraloperatoren auf streng q-konvexen Gebieten in Cn.
Boundary values of functions in Cegrell’s class
We study boundary values of functions in Cegrell’s class .
Boundary values of holomorphic functions and Cauchy problem for operator in the polydisc