Regularity and modulus of continuity of space-filling curves

DOI10.1007/s11854-018-0066-3zbMath1423.28014OpenAlexW2904584570WikidataQ109744291 ScholiaQ109744291MaRDI QIDQ2000387

Aleksandra Zapadinskaya, Pekka Koskela, Aapo Kauranen

Publication date: 28 June 2019

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: http://urn.fi/URN:NBN:fi:jyu-202001201325

zbMATH Keywords

modulus of continuityPeano curvesweighted coverings

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Hausdorff and packing measures (28A78)

Related Items (2)

Dyadic norm Besov-type spaces as trace spaces on regular trees ⋮ Nowhere differentiability conditions on composites of Peano curves

Cites Work

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• Dimension gap under conformal mappings
• Space filling with metric measure spaces
• Sobolev Peano cubes
• Pointwise smoothness of space-filling functions
• Space-filling curves
• Hausdorff dimension and mean porosity
• Luzin's condition (N) and Sobolev mappings
• Peano cubes with derivatives in a Lorentz space
• Boundary blow-up under Sobolev mappings
• Dimension gap under Sobolev mappings
• Lusin's condition (N) and mappings of the class W1, n.
• Quasiconformal removability and the quasihyperbolic metric

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