Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sequences of analytic disks   The subject considered in this paper has, at least, three points of interest.
Suppose that we have a sequence of one-dimensional analytic varieties in a
domain in $\Bbb C^n$. The cluster of this sequence consists from all points in
the domains such that every neighbourhood of such points intersects with
infinitely many different varieties. The first question is: what analytic
properties does the cluster inherit from varieties? We give a sufficient
criterion when the cluster contains an analytic disk, but it follows from
examples of Stolzenberg and Wermer that, in general, clusters can contain no
analytic disks. So we study algebras of continuous function on clusters, which
can be approximated by holomorphic functions or polynomials, and show that this
algebras possess some analytic properties in all but explicitly pathological
and uninteresting cases. Secondly, we apply and results about clusters to
polynomial hulls and maximal functions, finding remnants of analytic structures
there too. And, finally, due to more and more frequent appearances of analytic
disks as tools in complex analysis, it seems to be interesting to look at their
sequences to establish terminology, basic notation and properties.

8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys