Dan Coman

Extension of plurisubharmonic functions with growth control

Abstract Suppose that X is an analytic subvariety of a Stein manifold M and that φ is a plurisubharmonic (psh) function on X which is dominated by a continuous psh exhaustion function u of M. Given any number c > 1, we show that φ admits a psh extension to M which is dominated by cu+ on M. We use this result to prove that any ω-psh function on a subvariety of the complex projective space is the restriction of a global ω-psh function, where ω is the Fubini–Study Kähler form.

Quasianalyticity and pluripolarity

be the graph of / in C2. The set Tf is always pluripolar when / is a real analytic function. In [DF], Diederich and Fornaess give an example of a C?? function / with nonpluripolar graph in C2. The paper [LMP] contains an example of a holomorphic function / on the unit disk U, continuous up to the boundary, such that the graph of / over S is not pluripolar as a subset of C2. Thus a priori the pluripolarity of graphs of functions on S is indeterminate. In this paper we prove that graphs of quasianalytic functions are still pluripolar (all necessary definitions can be found in the next section). More precisely,

Quasiplurisubharmonic Green functions

Abstract Given a compact Kahler manifold X, a quasiplurisubharmonic function is called a Green function with pole at p ∈ X if its Monge–Ampere measure is supported at p. We study in this paper the existence and properties of such functions, in connection to their singularity at p. A full characterization is obtained in concrete cases, such as (multi)projective spaces.

Equidistribution for sequences of line bundles on normal Kähler spaces

We study the asymptotics of Fubini-Study currents and zeros of random holomorphic sections associated to a sequence of singular Hermitian line bundles on a compact normal Kaehler complex space.

Some Properties of Starlike Functions with Respect to Symmetric-Conjugate Points

Let A be tile class of all analytic functions in the unit disk U such that f(0)=f′(0)−1=0. A function f∈A is called starlike with respect to 2n symmetric-conjugate points if Rezf′(z)/fn(z)>0 for z∈U, where fn(z)=12n∑k=0n−1[ω−kf(ωkz)

CONVERGENCE OF FUBINI-STUDY CURRENTS FOR ORBIFOLD LINE BUNDLES

We discuss positive closed currents and Fubini-Study currents on orbifolds, as well as Bergman kernels of singular Hermitian orbifold line bundles. We prove that the Fubini-Study currents associated to high powers of a semipositive singular line bundle converge weakly to the curvature current on the set where the curvature is strictly positive, generalizing a well-known theorem of Tian. We include applications to the asymptotic distribution of zeros of random holomorphic sections.

Boundary behavior of the pluricomplex green function

AbstractLet Ω be a bounded domain inCn. This paper deals with the study of the behavior of the pluricomplex Green functiongΩ(z, w) when the polew tends to a boundary pointw0 of Ω. We find conditions on Ω which ensure that limw→wogΩ(z, w)=0, uniformly with respect toz on compact subsets of

INVARIANT CURRENTS AND DYNAMICAL LELONG NUMBERS

\bar \Omega \backslash \{ w_0 \}