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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übereinkommen, betreffend die AusweisbücherIn this chapter we review the definitions of Sobolev spaces, BV functions and perimeter of a set relative to the sub-Riemannian structure of ?. 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.

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übereinkommen, betreffend die AusweisbücherThe isoperimetric inequality in ? with respect to the horizontal perimeter was first proved by Pansu. We first state it in the setting of . sets.

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Horizontal Geometry of Submanifolds,This chapter is devoted to the study of the sub-Riemannian geometry of codimension 1 smooth submanifolds of the Heisenberg group.

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,The Isoperimetric Inequality in ?,The isoperimetric inequality in ? with respect to the horizontal perimeter was first proved by Pansu. We first state it in the setting of . sets.

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https://doi.org/10.1007/978-3-7643-8133-2Cauchy-Riemann manifold; Riemannian geometry; Sobolev space; contact geometry; differential geometry; evo

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Luca Capogna,Scott D. Pauls,Donatella Danielli,JerPresents a detailed description of Heisenberg submanifold geometry and geometric measure theory.Collects for the first time the various known partial results and methods of attack on Pansu‘s problem.I

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Progress in Mathematicshttp://image.papertrans.cn/a/image/155553.jpg