%0 Journal Article %1 pinkall1993computing %A Pinkall, U. %A Polthier, K. %D 1993 %I Taylor & Francis %J Experimental mathematics %K dirichlet.energy %N 1 %P 15--36 %R 10.1080/10586458.1993.10504266 %T Computing discrete minimal surfaces and their conjugates %V 2 %X We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in $\R^3$, $\Sph ^3$ and $\H^3$. The algorithm makes no restriction on the genus and can handle singular triangulations. Additionally, we present an algorithm that, starting from a discrete harmonic map, gives a conjugate harmonic map. This can be applied to the identity map on a minimal surface to produce its conjugate minimal surface, a procedure that often yields unstable solutions to a free boundary value problem for minimal surfaces. Symmetry properties of boundary curves are respected during conjugation.

@article{pinkall1993computing, abstract = {We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in $\R^3$, $\Sph ^3$ and $\H^3$. The algorithm makes no restriction on the genus and can handle singular triangulations. Additionally, we present an algorithm that, starting from a discrete harmonic map, gives a conjugate harmonic map. This can be applied to the identity map on a minimal surface to produce its conjugate minimal surface, a procedure that often yields unstable solutions to a free boundary value problem for minimal surfaces. Symmetry properties of boundary curves are respected during conjugation.}, added-at = {2012-12-30T00:34:20.000+0100}, author = {Pinkall, U. and Polthier, K.}, biburl = {https://www.bibsonomy.org/bibtex/2dc1ef500fa94335a460369361ec63ed7/ytyoun}, doi = {10.1080/10586458.1993.10504266}, interhash = {2abcea7ff045db8bff287acd0f105376}, intrahash = {dc1ef500fa94335a460369361ec63ed7}, journal = {Experimental mathematics}, keywords = {dirichlet.energy}, number = 1, pages = {15--36}, publisher = {Taylor \& Francis}, timestamp = {2012-12-30T00:34:20.000+0100}, title = {Computing discrete minimal surfaces and their conjugates}, volume = 2, year = 1993 }