Sobolev and BV Spaces
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.
KeywordsSobolev Space Heisenberg Group Representation Formula Carnot Group Perimeter Measure
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