Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups
| Autor: | Katrin Fässler, Daniela Di Donato |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
01 natural sciences
matemaattinen analyysi Combinatorics Corona (optical phenomenon) Mathematics - Metric Geometry 0103 physical sciences Heisenberg group Classical Analysis and ODEs (math.CA) FOS: Mathematics Mathematics::Metric Geometry 0101 mathematics Commutative property Physics Applied Mathematics Heisenberg groups 010102 general mathematics Metric Geometry (math.MG) Lipschitz continuity Graph corona decomposition Mathematics - Classical Analysis and ODEs 35R03 26A16 28A75 low-dimensional intrinsic Lipschitz graphs 010307 mathematical physics mittateoria Lipschitz extension |
| Popis: | This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group $\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every intrinsic $L$-Lipschitz graph over a subset of a $k$-dimensional horizontal subgroup $\mathbb{V}$ of $\mathbb{H}^n$ can be extended to an intrinsic $L'$-Lipschitz graph over the entire subgroup $\mathbb{V}$, where $L'$ depends only on $L$, $k$, and $n$. We further prove that $1$-dimensional intrinsic $1$-Lipschitz graphs in $\mathbb{H}^n$, $n\in \mathbb{N}$, admit corona decompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants. This complements results that were known previously only in the first Heisenberg group $\mathbb{H}^1$. The main difference to this case arises from the fact that for $1\leq k Comment: 30 pages; v2: minor revision, results unchanged |
| Databáze: | OpenAIRE |
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