Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups
Di Donato, D., & Fässler, K. (2021). Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups. Annali di Matematica Pura ed Applicata, Early online. https://doi.org/10.1007/s10231-021-01124-3
Published inAnnali di Matematica Pura ed Applicata
© 2021 the Authors
This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group Hn, n∈N. For 1⩽k⩽n, we show that every intrinsic L-Lipschitz graph over a subset of a k-dimensional horizontal subgroup V of Hn can be extended to an intrinsic L′-Lipschitz graph over the entire subgroup V, where L′ depends only on L, k, and n. We further prove that 1-dimensional intrinsic 1-Lipschitz graphs in Hn, n∈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 H1. The main difference to this case arises from the fact that for 1⩽k
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Related funder(s)Academy of Finland
Funding program(s)Research post as Academy Research Fellow, AoF
Additional information about fundingOpen access funding provided by Scuola Internazionale Superiore di Studi Avanzati - SISSA within the CRUI-CARE Agreement.
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