Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H\"older Regularity of Geometric Subdivision Schemes   We present a framework for analyzing non-linear $\mathbb{R}^d$-valued
subdivision schemes which are geometric in the sense that they commute with
similarities in $\mathbb{R}^d$. It admits to establish
$C^{1,\alpha}$-regularity for arbitrary schemes of this type, and
$C^{2,\alpha}$-regularity for an important subset thereof, which includes all
real-valued schemes. Our results are constructive in the sense that they can be
verified explicitly for any scheme and any given set of initial data by a
universal procedure. This procedure can be executed automatically and
rigorously by a computer when using interval arithmetics.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph