Abstract
This chapter is the core of this survey. We recall the definition of isoperimetric profile of ℍ and Pansu’s 1982 conjecture. Next we present a proof of the existence of an isoperimetric profile and describe some of the existing literature on the isoperimetric problem. Our aim is to reveal the main ideas and outlines of the proofs of various partial results and sketch some further techniques and methods which may lead to a solution, in order to guide the reader through the literature and to give a sense of the larger ideas that are in play.
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© 2007 Birkhäuser Verlag AG
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(2007). The Isoperimetric Profile of ℍ. In: Tyson, J.T. (eds) An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem. Progress in Mathematics, vol 259. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8133-2_8
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DOI: https://doi.org/10.1007/978-3-7643-8133-2_8
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8132-5
Online ISBN: 978-3-7643-8133-2
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