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Full-Text Articles in Physical Sciences and Mathematics
Regularity Of Non-Characteristic Minimal Graphs In The Heisenberg Group ā1, Luca Capogna, Giovanna Citti, Maria Manfredini
Regularity Of Non-Characteristic Minimal Graphs In The Heisenberg Group ā1, Luca Capogna, Giovanna Citti, Maria Manfredini
Mathematics Sciences: Faculty Publications
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 Cā regularity of the sub-Riemannian minimal surface along its Legendrian foliation.
Generalized Mean Curvature Flow In Carnot Groups, Luca Capogna, Giovanna Citti
Generalized Mean Curvature Flow In Carnot Groups, Luca Capogna, Giovanna Citti
Mathematics Sciences: Faculty Publications
In this paper we study the generalized mean curvature flow of sets in the sub-Riemannian geometry of Carnot groups. We extend to our context the level sets method and the weak (viscosity) solutions introduced in the Euclidean setting in [4] and [12]. We establish two special cases of the comparison principle, existence, uniqueness and basic geometric properties of the flow.