Convex isoperimetric sets in the Heisenberg group
By Roberto Monti, Matthieu Rickly. 2006
64 citations recorded by the source corpus.
We characterize convex isoperimetric sets in the Heisenberg group. We first prove Sobolev regularity for a certain class of R 2 -valued vector fields of bounded variation in the plane related to the curvature equations. Then we show that the boundary of convex isoperimetric sets is foliated by geodesics of the Carnot-Carath´ eodory distance.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/586aed8862ea2bcc28f741727bc638439726e256
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Manuel Ritor'e
- Jih-Hsin Cheng
- Jenn-Fang Hwang
- Paul Yang
- César Rosales
- Scott D. Pauls
- Giovanna Citti
- Maria Manfredini
Citations in the corpus
- Regularity of C1 smooth surfaces with prescribed p-mean curvature in the Heisenberg group (2007, methodology): “Later Monti and Rickly ([ 15 ]) obtained the same result for convex isoperimetric sets without regularity assumptions.”
- Area-stationary surfaces in the Heisenberg group H1 (2005, background): “In [ MoR ] it is proved that the \ball sets" bounded by the spheres S solve the isoperimetric problem in the class of sets of H1 which are convex in the Euclidean sense.”