Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On S.L. Tabachnikov's conjecture   S. L. Tabachnikov's conjecture is proved: for any closed curve $\Gamma$ lying
inside convex closed curve $\Gamma_1$ the mean absolute curvature $T(\Gamma)$
exceeds $T(\Gamma_1)$ if $\Gamma\ne k\Gamma_1$. An inequality $T(\Gamma)\ge
T(\Gamma_1)$ is proved for curves in a hemisphere.

24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin