English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Pro

Presents the zaia usage as premium feature

ZAIA

Presents AI Discovery search usage as a premium feature

AI Discovery

Presents AI Discovery explain and summary usage as a premium feature

Content Analysis

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Presents the pdf analysis as premium feature

PDF Analysis

1500 Top-up

3000 Top-up

Zendy Basic

2500 Top-up

Zendy Unlimited

Presents the access of premium content as premium feature

Premium Content

Two triangle meshes are conformally equivalent if for any pair of incidenttriangles the absolute values of the corresponding cross-ratios of the fourvertices agree. Such a pair can be considered as preimage and image of adiscrete conformal map. In this article we study discrete conformal maps whichare defined on parts of a triangular lattice $T$ with strictly acute angles.That is, $T$ is an infinite triangulation of the plane with congruent strictlyacute triangles. A smooth conformal map $f$ can be approximated on a compactsubset 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 triangularlattices, in "Advances in Discrete Differential Geometry" (A.I. Bobenko ed.),Springer (2016), 133--149]. We improve this result and show that theconvergence is in fact in $C^\infty$. Furthermore, we describe how thecross-ratios of the four vertices for pairs of incident triangles are relatedto the Schwarzian derivative of $f$.

$C^\infty$-convergence of conformal mappings on triangular lattices