Lipschitz Functions on Submanifolds of Heisenberg Groups
نویسندگان
چکیده
Abstract We study the behavior of Lipschitz functions on intrinsic $C^1$ submanifolds Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. also provide two applications: a Lusin-type approximation ${\mathbb {H}}$-rectifiable sets and coarea formula that completes program started in [18].
منابع مشابه
Intrinsic Lipschitz Graphs in Heisenberg Groups
In the last few years there have been a fairly large amount of work dedicated to the study of intrinsic submanifolds of various dimension and codimension inside the Heisenberg groups H or more general Carnot groups. For example intrinsically C surfaces, rectifiable sets, finite perimeter sets, various notions of convex surfaces have been studied. Here and in what follows, intrinsic will denote ...
متن کاملThe Fourier Transforms of Lipschitz Functions on the Heisenberg Group
We study the order of magnitude of the Fourier transforms of certain Lipschitz functions on the Heisenberg group Hn. We compare our conclusions with some previous results in the field.
متن کاملSmoothness of Lipschitz Minimal Intrinsic Graphs in Heisenberg Groups
We prove that Lipschitz intrinsic graphs in the Heisenberg groups Hn, with n > 1, which are vanishing viscosity solutions of the minimal surface equation are smooth.
متن کاملRegular Submanifolds, Graphs and Area Formula in Heisenberg Groups
We describe intrinsically regular submanifolds in Heisenberg groups H. Low dimensional and low codimensional submanifolds turn out to be of a very different nature. The first ones are Legendrian surfaces, while low codimensional ones are more general objects, possibly non Euclidean rectifiable. Nevertheless we prove that they are graphs in a natural group way, as well as that an area formula ho...
متن کاملIntrinsic Regular Submanifolds in Heisenberg Groups Are Differentiable Graphs
We characterize intrinsic regular submanifolds in the Heisenberg group as intrinsic differentiable graphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2022
ISSN: ['1687-0247', '1073-7928']
DOI: https://doi.org/10.1093/imrn/rnac066