Regularity of non-characteristic minimal graphs in the Heisenberg group $\mathbb{H}^{1}$ Luca CapognaGiovanna CittiMaria Manfredini 35H2053A1053C17minimal surfacessub-Riemannian geometryviscosity solutions Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian approximation scheme, as limit of Riemannian minimal surfaces. We study the regularity of Lipschitz, non-characteristic minimal surfaces which arise as such limits. Our main results are a-priori estimates on the solutions of the approxi mating Riemannian PDE and the ensuing $C^{\infty}$ regularity of the sub-Riemannian minimal surface along its Legendrian foliation. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3673 10.1512/iumj.2009.58.3673 en Indiana Univ. Math. J. 58 (2009) 2115 - 2160 state-of-the-art mathematics http://iumj.org/access/