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Differentiability of Intrinsic Lipschitz Functions within Heisenberg Groups

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Abstract

We study the notion of intrinsic Lipschitz graphs within Heisenberg groups, focusing our attention on their Hausdorff dimension and on the almost everywhere existence of (geometrically defined) tangent subgroups. In particular, a Rademacher type theorem enables us to prove that previous definitions of rectifiable sets in Heisenberg groups are natural ones.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, Piazza di porta San Donato, 5, 40126, Bologna, Italy

    Bruno Franchi

  2. Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38050, Povo (Trento), Italy

    Raul Serapioni & Francesco Serra Cassano

Authors
  1. Bruno Franchi
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  2. Raul Serapioni
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  3. Francesco Serra Cassano
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Corresponding author

Correspondence to Bruno Franchi.

Additional information

Communicated by Vern Paulsen.

B. Franchi is supported by MURST, Italy and by University of Bologna, Italy, funds for selected research topics.

R. Serapioni is supported by MURST, Italy and University of Trento, Italy.

F. Serra Cassano is supported by MURST, Italy and University of Trento, Italy.

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Franchi, B., Serapioni, R. & Serra Cassano, F. Differentiability of Intrinsic Lipschitz Functions within Heisenberg Groups. J Geom Anal 21, 1044–1084 (2011). https://doi.org/10.1007/s12220-010-9178-4

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  • DOI: https://doi.org/10.1007/s12220-010-9178-4

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