We study the behavior of Lipschitz functions on intrinsic C1 submanifolds of Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. We also provide two applications: a Lusin-type approximation of Lipschitz functions on H-rectifiable sets and a coarea formula on ℍ-rectifiable sets that completes the program started in [18].
Lipschitz Functions on Submanifolds of Heisenberg Groups
Julia, Antoine;Nicolussi Golo, Sebastiano;Vittone, Davide
2023
Abstract
We study the behavior of Lipschitz functions on intrinsic C1 submanifolds of Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. We also provide two applications: a Lusin-type approximation of Lipschitz functions on H-rectifiable sets and a coarea formula on ℍ-rectifiable sets that completes the program started in [18].
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