Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds
Separately superharmonic functions in product networks
Let X×Y be the Cartesian product of two locally finite, connected networks that need not have reversible conductance. If X,Y represent random walks, it is known that if X×Y is recurrent, then X,Y are both recurrent. This fact is proved here by non-probabilistic methods, by using the properties of separately superharmonic functions. For this class of functions on the product network X×Y, the Dirichlet solution, balayage, minimum principle etc. are obtained. A unique integral representation is given...
Seperable maximal pluriharmonic functions in two complex variables.
Siciak’s extremal function of convex sets in
Singular sets of separately analytic functions
Small sets in
Smooth, but not Complex-Analytic Pluripolar Sets.
Smooth Plurisubharmonic Functions Without Subextension.
Smoothing Plurisubharmonic Functions on Complex Spaces.
Smoothness of Green's functions and Markov-type inequalities
Let E be a compact set in the complex plane, be the Green function of the unbounded component of with pole at infinity and where the supremum is taken over all polynomials of degree at most n, and . The paper deals with recent results concerning a connection between the smoothness of (existence, continuity, Hölder or Lipschitz continuity) and the growth of the sequence . Some additional conditions are given for special classes of sets.
Solving the Degenerate Complex Monge-Ampère Equation with One Concentrated Singularity.
Some applications of the trace condition for pluriharmonic functions in Cn.
In this paper we investigate some applications of the trace condition for pluriharmonic functions on a smooth, bounded domain in Cn. This condition, related to the normal component on ∂D of the ∂-operator, permits us to study the Neumann problem for pluriharmonic functions and the ∂-problem for (0,1)-forms on D with solutions having assigned real part on the boundary.
Some Characterizations of L-regular Points.
Some characterizations of the class and applications
We give some characterizations of the class and use them to establish a lower estimate for the log canonical threshold of plurisubharmonic functions in this class.
Some convexity properties of morphisms of complex spaces.
Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator
We find a bounded solution of the non-homogeneous Monge-Ampère equation under very weak assumptions on its right hand side.
Splitting of the ∂-complex in weighted spaces of square integrable functions.
Stabilité de la classe des variétés Kählériennes par certains morphismes propres.
Stability of the Monge-Ampère Foliation.
Stochastic characterization of plurisubharmonicity and convexity of functions
It is described how both plurisubharmonicity and convexity of functions can be characterized in terms of simple to work with classes of holomorphic martingales, namely a class of driftless Itô processes satisfying a skew-symmetry property and a family of linear modifications of Brownian motion parametrized by a compact set.