Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free boundaries subject to topological constraints   We discuss the extent to which solutions to one-phase free boundary problems
can be characterized according to their topological complexity. Our questions
are motivated by fundamental work of Luis Caffarelli on free boundaries and by
striking results of T. Colding and W. Minicozzi concerning finitely connected,
embedded, minimal surfaces. We review our earlier work on the simplest case,
one-phase free boundaries in the plane in which the positive phase is simply
connected. We also prove a new, purely topological, effective removable
singularities theorem for free boundaries. At the same time, we formulate some
open problems concerning the multiply connected case and make connections with
the theory of minimal surfaces and semilinear variational problems.

36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat