Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monotone and convex restrictions of continuous functions   Suppose that $f$ belongs to a suitably defined complete metric space $ {{\cal
C}}^{{\alpha}}$ of H\"older $ {\alpha}$-functions defined on $[0,1]$. We are
interested in whether one can find large (in the sense of Hausdorff, or
lower/upper Minkowski dimension) sets $A {\subset} [0,1]$ such that $f|_{A}$ is
monotone, or convex/concave. Some of our results are about generic functions in
$ {{\cal C}}^{{\alpha}}$ like the following one: we prove that for the generic
$f\in C_{1}^{{\alpha}}[0,1]$, $0\leq {\alpha}<2$ for any $A {\subset} [0,1]$
such that $f|_{A}$ is convex, or concave we have ${\mathrm{dim}}_{\mathrm H}
A\leq \underline{\mathrm{dim}}_M A\leq \max \{0, {\alpha}-1 \}.$ On the other
hand, we also have some results about all functions belonging to a certain
space. For example the previous result is complemented by the following one:
for $1< {\alpha}\leq 2$ for any $f\in C^{{\alpha}}[0,1]$ there is always a set
$A {\subset}[0,1]$ such that ${\mathrm{dim}}_{\mathrm H} A= {\alpha}-1$ and
$f|_{A}$ is convex, or concave on $A$.

14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph