Quantitative isoperimetric inequalities in H^n
Valentina Franceschi, Gian Paolo Leonardi, Roberto Monti
TL;DR
This paper establishes quantitative isoperimetric inequalities in the Heisenberg group H^n, focusing on Pansu's spheres, using sub-calibrations to compare sets and quantify deviations from optimal shapes.
Contribution
It provides the first quantitative inequalities for isoperimetric sets in H^n, specifically for Pansu's spheres, under certain restrictions.
Findings
Quantitative inequalities are proven for Pansu's spheres in H^n.
The proof employs sub-calibrations to compare sets.
Results quantify how sets deviate from isoperimetric shapes.
Abstract
In the Heisenberg group H^n, we prove quantitative isoperimetric inequalities for Pansu's spheres, that are known to be isoperimetric under various assumptions. The inequalities are shown for suitably restricted classes of competing sets and the proof relies on the construction of sub-calibrations.
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