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Tangent Halfspaces to Sets of Finite Perimeter in Carnot Groups

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Advances in Phase Space Analysis of Partial Differential Equations

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 78))

Summary

We consider sets of locally finite perimeter in Carnot groups. We show that if E is a set of locally finite perimeter in a Carnot group G then, for almost every x ∈ G with respect to the perimeter measure of E, some tangent of E at x is a vertical halfspace. This is a partial extension of a theorem of Franchi-Serapioni-Serra Cassano in step 2 Carnot groups.

2000 AMS Subject Classification: 53C17, 49Q15.

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Authors and Affiliations

  1. Scuola Normale Superiore, piazza dei Cavalieri, 7, 56100, Pisa, Italy

    Luigi Ambrosio

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  1. Luigi Ambrosio
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Correspondence to Luigi Ambrosio .

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Editors and Affiliations

  1. Dipto. Matematica, Università di Bologna, Piazza di Porta San Donato 5, Bologna, 40126, Italy

    Antonio Bove

  2. Dipto. Scienze Matematiche, Università di Trieste, via A. Valerio 12/1, Trieste, 34127, Italy

    Daniele Del Santo

  3. Dipto. Matematica, Università Pisa, Largo Bruno Pontecorvo 5, Pisa, 56127, Italy

    M.K. Venkatesha Murthy

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Ambrosio, L. (2009). Tangent Halfspaces to Sets of Finite Perimeter in Carnot Groups. In: Bove, A., Del Santo, D., Murthy, M. (eds) Advances in Phase Space Analysis of Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 78. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4861-9_1

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