Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Several Metric Properties of Level Curves   This article establishes several remarkably simple identities relating
certain metric invariants of level curves of real and complex functions. In
particular, we relate lengths of level curves to their curvature and to the
gradient field of the function. Some geometric and analytic applications of the
results are shown.

27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys