Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The filling law: a general framework for leaf shape diversity and its
  consequences on folded leaves   Leaves are packed in a bud in different ways, being flat, enrolled, or
folded, but always filling the whole bud volume. This {\guillemotleft} filling
law {\guillemotright} has many consequences, in particular on the shape of
growing folded leaves. This is shown here for different types of folding and
packing. The folded volume is always part of an ellipsoid, with the veins on
the outside rounded face, and the lamina margin on an adaxial plane or axis.
The veins on the abaxial side protect the more fragile lamina. The first
general consequence of the folds is the presence of symmetries on the leaf
shape, but also quantitative relationships between lobes and sinus sizes. For
particular geometries, the leaf lamina can be limited by lateral veins,
creating spoon-like lobes, or transverse cuts, creating asymmetrical wavy
perimeters. A change in the packing between cultivars induces the corresponding
change in the leaf shape. Each particular case shows how pervasive are the
geometrical consequences of the filling law.

21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat