Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Valuative analysis of planar plurisubharmonic functions   We show that valuations on the ring R of holomorphic germs in dimension 2 may
be naturally evaluated on plurisubharmonic functions, giving rise to
generalized Lelong numbers in the sense of Demailly. Any plurisubharmonic
function thus defines a real-valued function on the set V of valuations on R
and--by way of a natural Laplace operator defined in terms of the tree
structure on V--a positive measure on V. This measure contains a great deal of
information on the singularity at the origin. Under mild regularity
assumptions, it yields an exact formula for the mixed Monge-Ampere mass of two
plurisubharmonic functions. As a consequence, any generalized Lelong number can
be interpreted as an average of valuations. Using our machinery we also show
that the singularity of any positive closed (1,1) current T can be attenuated
in the following sense: there exists a finite composition of blowups such that
the pull-back of T decomposes into two parts, the first associated to a divisor
with normal crossing support, the second having small Lelong numbers.

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The categories of this paper are: nlin
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph