64 research outputs found
Subextension of plurisubharmonic functions with weak singularities
We prove several results showing that plurisubharmonic functions with various
bounds on their Monge-Ampere masses on a bounded hyperconvex domain always
admit global plurisubharmonic subextension with logarithmic growth at infinity
Maximal subextensions of plurisubharmonic functions
In this paper we are concerned with the problem of local and global
subextensions of (quasi-)plurisubharmonic functions from a "regular" subdomain
of a compact K\"ahler manifold. We prove that a precise bound on the complex
Monge-Amp\`ere mass of the given function implies the existence of a
subextension to a bigger regular subdomain or to the whole compact manifold. In
some cases we show that the maximal subextension has a well defined complex
Monge-Amp\`ere measure and obtain precise estimates on this measure. Finally we
give an example of a plurisubharmonic function with a well defined
Monge-Amp\`ere measure and the right bound on its Monge-Amp\`ere mass on the
unit ball in \C^n for which the maximal subextension to the complex
projective space \mb P_n does not have a globally well defined complex
Monge-Amp\`ere measure
Weighted pluricomplex energy
We study the complex Monge-Ampre operator on the classes of finite
pluricomplex energy in the general case
( i.e. the total Monge-Ampre mass may be infinite). We establish an
interpretation of these classes in terms of the speed of decrease of the
capacity of sublevel sets and give a complete description of the range of the
operator on the classes Comment: Contrary to what we claimed in the previous version, in Theorem 5.1
we generalize some Theorem of Urban Cegrell but we do not give a new proof.
To appear in Potenial Analysi
Partial pluricomplex energy and integrability exponents of plurisubharmonic functions
We give a sufficient condition on the Monge-Amp\`ere mass of a
plurisubharmonic function for to be locally integrable. This
gives a pluripotential theoretic proof of a theorem by J-P. Demailly.Comment: extended version with new results and more application
Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates
First we prove a new inequality comparing uniformly the relative volume of a
Borel subset with respect to any given complex euclidean ball \B \sub \C^n
with its relative logarithmic capacity in \C^n with respect to the same ball
\B.
An analoguous comparison inequality for Borel subsets of euclidean balls of
any generic real subspace of \C^n is also proved.
Then we give several interesting applications of these inequalities.
First we obtain sharp uniform estimates on the relative size of \psh
lemniscates associated to the Lelong class of \psh functions of logarithmic
singularities at infinity on \C^n as well as the Cegrell class of
\psh functions of bounded Monge-Amp\`ere mass on a hyperconvex domain \W
\Sub \C^n.
Then we also deduce new results on the global behaviour of both the Lelong
class and the Cegrell class of \psh functions.Comment: 25 page
Oka's inequality for currents and applications
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46241/1/208_2005_Article_BF01446636.pd
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