Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $C^\infty$-convergence of conformal mappings on triangular lattices   Two triangle meshes are conformally equivalent if for any pair of incident
triangles the absolute values of the corresponding cross-ratios of the four
vertices agree. Such a pair can be considered as preimage and image of a
discrete conformal map. In this article we study discrete conformal maps which
are defined on parts of a triangular lattice $T$ with strictly acute angles.
That is, $T$ is an infinite triangulation of the plane with congruent strictly
acute triangles. A smooth conformal map $f$ can be approximated on a compact
subset by such discrete conformal maps $f^\varepsilon$, defined on a part of
$\varepsilon T$ for $\varepsilon>0$ small enough, see [U. B\"ucking,
Approximation of conformal mappings using conformally equivalent triangular
lattices, in "Advances in Discrete Differential Geometry" (A.I. Bobenko ed.),
Springer (2016), 133--149]. We improve this result and show that the
convergence is in fact in $C^\infty$. Furthermore, we describe how the
cross-ratios of the four vertices for pairs of incident triangles are related
to the Schwarzian derivative of $f$.

25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess