Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertex theorems for capillary drops on support planes   We consider a capillary drop that contacts several planar bounding walls so
as to produce singularities (vertices) in the boundary of its free surface. It
is shown under various conditions that when the number of vertices is less than
or equal to three, then the free surface must be a portion of a sphere. These
results extend the classical theorem of H. Hopf on constant mean curvature
immersions of the sphere. The conclusion of sphericity cannot be extended to
more than three vertices, as we show by examples.

29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics