From Grushin to Heisenberg via an isoperimetric problem

DOI10.1016/j.jmaa.2007.07.053zbMath1134.53016OpenAlexW1978889356WikidataQ125767481 ScholiaQ125767481MaRDI QIDQ2467756

Annalisa Baldi, Nicola Arcozzi

Publication date: 28 January 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.07.053

zbMATH Keywords

Heisenberg groupisoperimetric problemGrushin plane

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Sub-Riemannian geometry (53C17)

Related Items (7)

Dimension distortion by right coset projections in the Heisenberg group ⋮ Fundamental solution of a higher step Grushin type operator ⋮ Dimension distortion by Sobolev mappings in foliated metric spaces ⋮ Sub-Riemannian Geometry and Hypoelliptic Operators ⋮ Spectral analysis and geometry of a sub-Riemannian structure on \(S^3\) and \(S^7\) ⋮ Geometry of Grushin spaces ⋮ Existence of equilibrium for infinite system of interacting diffusions

Cites Work

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• Nonholonomic manifolds and nilpotent analysis
• A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds
• Hypoelliptic differential operators and nilpotent groups
• Isoperimetric inequality in the Grushin plane
• On the Dido problem and plane isoperimetric problems
• Some properties of Carnot-Carath'eodory balls in the Heisenberg group
• On the Grushin operator and hyperbolic symmetry
• Global analysis - studies and applications III. Transl. from the Russian

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