Examples of area-minimizing surfaces in the subriemannian Heisenberg group H^1 with low regularity

By Manuel Ritor'e. 2008

48 citations recorded by the source corpus.

We give new examples of entire area-minimizing t-graphs in the subriemannian Heisenberg group H^1. Most of the examples are locally lipschitz in Euclidean sense. Some regular examples have prescribed singular set consisting of either a horizontal line or a finite number of horizontal halflines extending from a given point. Amongst them, a large family of area-minimizing cones is obtained.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/47eca23f60a96d348b51a97a4b592468107c9108

How researchers see this paper

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In Applied Mathematics

1. Giovanna Citti
2. Maria Manfredini
3. Luca Capogna
4. Francesco Serra Cassano
5. A. Domokos

In Geometry and Topology

1. Luca Capogna
2. Giovanna Citti
3. Maria Manfredini

Citations in the corpus

• Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1 (2010, background): “Given our regularity result and the wealth of examples of area minimizers with low regularity constructed recently by Cheng, Hwang and Yang in [8], by Pauls in [34] and by Ritoré in [35], it is clear that not all minimal surfaces, not even those that are area minimizers arise as limits of Riemannian”