Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Plateau's Problem: What's Next   Plateau's problem is not a single conjecture or theorem, but rather an
abstract framework, encompassing a number of different problems in several
related areas of mathematics. In its most general form, Plateau's problem is to
find an element of a given collection \(\cal{C} \) of "surfaces" specified by
some boundary constraint, which minimizes, or is a critical point of, a given
"area" function \(F:\cal{C}\to \R \). In addition, one should also show that
any such element satisfies some sort of regularity, that it be a sufficiently
smooth manifold away from a well-behaved singular set. The choices apparent in
making this question precise lead to a great many different versions of the
problem. Plateau's problem has generated a large number of papers, inspired new
fields of mathematics, and given rise to techniques which have proved useful in
applications further afield. In this review we discuss a few highlights from
the past hundred years, with special attention to papers of Federer, Fleming,
Reifenberg and Almgren from the 1960's, and works by several groups, including
ourselves, who have made significant progress on different aspects of the
problem in recent years. A number of open problems are presented.

3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas