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Abstract

In this chapter we review the definitions of Sobolev spaces, BV functions and perimeter of a set relative to the sub-Riemannian structure of ℍ. These notions are crucial for the development of sub-Riemannian geometric measure theory. Our treatment here is brief, focusing only on those aspects most relevant for the isoperimetric problem.

Keywords

Sobolev Space Heisenberg Group Representation Formula Carnot Group Perimeter Measure 
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Copyright information

© Birkhäuser Verlag AG 2007

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