A characterization of bounded plurisubharmonic functions
We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.
A correction to and a remark on our paper "Remarks on the proof of a generalized Hartogs Lemma" (Ann. Polon. Math. 70 (1998), 43-47)
A counterexample to the regularity of the degenerate complex Monge-Ampère equation
We modify an example due to X.-J. Wang and obtain some counterexamples to the regularity of the degenerate complex Monge-Ampère equation on a ball in ℂⁿ and on the projective space ℙⁿ.
A Criterion for the Neumann Type Problem over a Differential Complex on a Strongly Pseudo Convex Domain.
A decomposition of complex Monge-Ampère measures
We prove a decomposition theorem for complex Monge-Ampère measures of plurisubharmonic functions in connection with their pluripolar sets.
A deformation of commutative polynomial algebras in even numbers of variables
We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the interchanges of right and left total symbols of differential operators of polynomial algebras. Furthermore, a more conceptual re-formulation for the image conjecture [18] is also given in terms of the deformed algebras. Consequently, the well-known Jacobian conjecture...
A general Dirichlet problem for the complex Monge-Ampère operator
We study a general Dirichlet problem for the complex Monge-Ampère operator, with maximal plurisubharmonic functions as boundary data.
A Hilbert Lemniscate Theorem in
For a regular, compact, polynomially convex circled set in , we construct a sequence of pairs of homogeneous polynomials in two variables with
A note on Berezin-Toeplitz quantization of the Laplace operator
Given a Hodge manifold, it is introduced a self-adjoint operator on the space of endomorphisms of the global holomorphic sections of the polarization line bundle. Such operator is shown to approximate the Laplace operator on functions when composed with Berezin-Toeplitz quantization map and its adjoint, up to an error which tends to zero when taking higher powers of the polarization line bundle.
A note on the Hörmander, Donnelly-Fefferman, and Berndtsson L²-estimates for the ∂̅-operator
We give upper and lower bounds for constants appearing in the L²-estimates for the ∂̅-operator due to Donnelly-Fefferman and Berndtsson.
A Note on the kernel of the ...-Neumann operator on strongly pseudoconvex domains.
A note on the regularity of the degenerate complex Monge-Ampère equation
We prove the almost regularity of the degenerate complex Monge-Ampère equation in a special case.
A priori estimates for weak solutions of complex Monge-Ampère equations
Let be a compact Kähler manifold and be a smooth closed form of bidegree which is nonnegative and big. We study the classes of -plurisubharmonic functions of finite weighted Monge-Ampère energy. When the weight has fast growth at infinity, the corresponding functions are close to be bounded. We show that if a positive Radon measure is suitably dominated by the Monge-Ampère capacity, then it belongs to the range of the Monge-Ampère operator on some class . This is done by establishing...
A pseudoconvex domain with bounded solutions for ..., but not admitting ...-estimates.
A Realization Problem in the Theory of Analytic curves
A regularity theorem for the complex Monge-Ampère equation in ℂPⁿ
regularity of the solutions of the complex Monge-Ampère equation in ℂPⁿ with the n-root of the right hand side in is proved.
A Remark on a Paper by S.R. Bell.
A result on the comparison principle for the log canonical threshold of plurisubharmonic functions
We prove a comparison principle for the log canonical threshold of plurisubharmonic functions under an assumption on complex Monge-Ampère measures.
A Riemann-Roch-Hirzebruch formula for traces of differential operators
Let be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an -dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology of the algebra of differential operators on a formal neighbourhood of a...
A Simplification and Extension of Fefferman's Theorem on Biholomorphic Mappings.