%0 Generic %1 georgakopoulos2019convergence %A Georgakopoulos, Agelos %A Panagiotis, Christoforos %D 2019 %K complex_analysis conformal_mappings graphs tilings %T Convergence of square tilings to the Riemann map %U http://arxiv.org/abs/1910.06886 %X A well-known theorem of Rodin & Sullivan, previously conjectured by Thurston, states that the circle packing of the intersection of a lattice with a simply connected planar domain $Ømega$ into the unit disc $D$ converges to a Riemann map from $Ømega$ to $D$ when the mesh size converges to 0. We prove the analogous statement when circle packings are replaced by the square tilings of Brooks et al.

@preprint{georgakopoulos2019convergence, abstract = {A well-known theorem of Rodin \& Sullivan, previously conjectured by Thurston, states that the circle packing of the intersection of a lattice with a simply connected planar domain $\Omega$ into the unit disc $\mathbb{D}$ converges to a Riemann map from $\Omega$ to $\mathbb{D}$ when the mesh size converges to 0. We prove the analogous statement when circle packings are replaced by the square tilings of Brooks et al.}, added-at = {2021-05-11T22:27:50.000+0200}, author = {Georgakopoulos, Agelos and Panagiotis, Christoforos}, biburl = {https://www.bibsonomy.org/bibtex/22fa9ff9e11349f9abb072ff882dc43b3/lukas.geyer}, description = {Convergence of square tilings to the Riemann map}, interhash = {55f110a6a8dee95ba8545b724af7a917}, intrahash = {2fa9ff9e11349f9abb072ff882dc43b3}, keywords = {complex_analysis conformal_mappings graphs tilings}, note = {cite arxiv:1910.06886}, timestamp = {2021-05-11T22:27:50.000+0200}, title = {Convergence of square tilings to the Riemann map}, url = {http://arxiv.org/abs/1910.06886}, year = 2019 }