Regularity of Non-Characteristic Minimal Graphs in the Heisenberg Group ℍ¹

Authors

Luca Capogna, University of ArkansasFollow
Giovanna Citti, Alma Mater Studiorum Università di Bologna
Maria Manfredini, Alma Mater Studiorum Università di Bologna

Document Type

Article

Publication Date

12-1-2009

Publication Title

Indiana University Mathematics Journal

Abstract

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 apriori estimates on the solutions of the approximating Riemannian PDE and the ensuing C∞ regularity of the sub-Riemannian minimal surface along its Legendrian foliation.

Keywords

Minimal surfaces, Sub-Riemannian geometry, Viscosity solutions

Volume

58

Issue

5

First Page

2115

Last Page

2160

DOI

10.1512/iumj.2009.58.3673

ISSN

00222518

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Capogna, Luca; Citti, Giovanna; and Manfredini, Maria, "Regularity of Non-Characteristic Minimal Graphs in the Heisenberg Group ℍ¹" (2009). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/139