Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips

D. Danielli, N. Garofalo, D. M. Nhieu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We consider the class of minimal surfaces given by the graphical strips S in the Heisenberg group H1 and we prove that for points p along the center of H1 the quantity is monotone increasing. Here, Q is the homogeneous dimension of H1. We also prove that these minimal surfaces have maximum volume growth at infinity.

Original languageEnglish (US)
Pages (from-to)617-637
Number of pages21
JournalMathematische Zeitschrift
Volume265
Issue number3
DOIs
StatePublished - Jul 2010
Externally publishedYes

Keywords

  • First and second variation
  • H-mean curvature
  • Integration by parts
  • Minimal surfaces
  • Monotonicity of the H-perimeter

ASJC Scopus subject areas

  • Mathematics(all)

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