A. Lukyanenko

activity

20112025

most citedOn the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target

3 citations · 3 across the 10 of their papers we have counts for

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Showing 2011Show all

2 papers · 1 filter

math.GT2011

Bi-Lipschitz extension from boundaries of certain hyperbolic spaces

Anton Lukyanenko

Tukia and Vaisala showed that every quasi-conformal map of $R^{n}$ extends to a quasi-conformal self-map of $R^{n + 1}$ . The restriction of the extended map to the upper half-space $…

math.FA2011★ 3 cited

On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target

Noel DeJarnette, Piotr Hajlasz, Anton Lukyanenko +1

We study the question: when are Lipschitz mappings dense in the Sobolev space $W^{1, p} (M, H^{n})$ ? Here $M$ denotes a compact Riemannian manifold with or without boundary, wh…