Differentiable points of Sierpinski-like sponges

DOI10.1016/j.aim.2019.106936zbMath1431.28017OpenAlexW2995989698WikidataQ126593783 ScholiaQ126593783MaRDI QIDQ2288082

Li-Feng Xi

Publication date: 17 January 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2019.106936

zbMATH Keywords

self-similar setrectifiable setbilipschitz equivalencedifferentiable pointsSierpinski-like sponge

Mathematics Subject Classification ID

Fractals (28A80)

Related Items

Mean geodesic distance of the level-\(n\) Sierpinski gasket, AVERAGE DISTANCE OF SIERPINSKI-LIKE CARPET

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bilipschitz embedding of self-similar sets
• Affine embeddings and intersections of Cantor sets
• Dimension of slices of Sierpiński-like carpets
• Periodic billiard orbits of self-similar Sierpiński carpets
• Topological invariants and Lipschitz equivalence of fractal squares
• Lipschitz equivalence of a class of general Sierpinski carpets
• Harmonic measure and arclength
• Rectifiable sets and the traveling salesman problem
• Lipschitz equivalence of self-similar sets
• Self-similar sets with initial cubic patterns
• Intersecting random translates of invariant Cantor sets
• On the Hausdorff dimension of fibres
• On the shape of Cantor sets
• Manhattan property of geodesic paths on self-affine carpets
• Complexity of the Frobenius problem
• The Cauchy integral, analytic capacity, and uniform rectifiability
• Quasisymmetric rigidity of square Sierpiński carpets
• Topological structure of fractal squares
• Rectifiable curves in Sierpinski carpets
• Slicing the Sierpiński gasket
• On the dimensions of sections for the graph-directed sets
• Nontrivial paths and periodic orbits of theT-fractal billiard table
• Topological characterization of the Sierpiński curve
• The Hausdorff dimension of general Sierpiński carpets
• Ahlfors-David regular sets and bilipschitz maps
• Lipschitz equivalence of subsets of self-conformal sets
• On the Lipschitz equivalence of Cantor sets
• SOME ALGEBRAIC PROPERTIES OF SMALL SETS
• Dimension of slices through the Sierpinski carpet
• Fourier Analysis and Hausdorff Dimension
• On a linear diophantine problem of Frobenius
• DIMENSIONS OF INTERSECTIONS OF THE SIERPINSKI CARPET WITH LINES OF RATIONAL SLOPES
• On a Problem of Partitions