Titlebook: An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem; Luca Capogna,Scott D. Pauls,Donatella Danielli,Jer B

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Der deutsch-?sterreichische Postvereinntroduce the horizontal subbundle (which we think of as .) and present the Carnot-Carathéodory metric as the least time required to travel between two given points at unit speed along horizontal paths. Subsequently we introduce the notion of sub-Riemannian metric and show how it arises from degenera

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Der deutsch-?sterreichische Postvereinchanging from point to point. If the constraints are too tight, then it may be impossible to join any two points with an admissible trajectory, hence one needs to find conditions on the constraints implying “horizontal accessibility”.

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https://doi.org/10.1007/978-3-642-45719-7ity. As shown in Section 7.1, the best constant for the isoperimetric inequality agrees with the best constant for the geometric (.-) Sobolev inequality. Recall that in the context of the Heisenberg group, the .-Sobolev inequalities take the form . In this chapter we discuss sharp constants for othe

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An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem978-3-7643-8133-2Series ISSN 0743-1643 Series E-ISSN 2296-505X

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