Document Type

Article

Publication Date

1-1-2007

Publication Title

Lecture Notes of Seminario Interdisciplinare di Matematica

Abstract

We formulate the isoperimetric problem for the class of C2 smooth cylindrically symmetric surfaces in the Heisenberg group in terms of Legendrian foliations. The known results for the sub-Riemannian isoperimetric problem yield a new isoperimetric inequality in the plane: For any strictly convex, C2 loop γ ∈ R2 , bounding a planar region ω, we have I(ω) 3 4 ≤ √ π 3 1 4 (8π) 3 4 L3, where I(ω) = R ω |z| 2dz is the moment of inertia and L3 is the length of the curve γ 3 . Moreover if equality is achieved then γ is a circle.

Volume

6

First Page Number

93

Last Page Number

106

Version

Preprint

Rights

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.

Included in

Mathematics Commons

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