Cartesian products of the Sierpiński carpet (and similar self-similar fractals) with itself at least twice do not attain their conformal dimension.
Construction of self-similar energy forms and singularity of S obolev spaces on L aakso-type fractal spaces
4 Pith papers cite this work. Polarity classification is still indexing.
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On Ahlfors-regular ε-snowtrees the discrete-energy Sobolev space equals the Korevaar–Schoen space for every multiscale partition, with critical exponent α_p = Q/p + 1/ε − 1/(pε).
Constructs canonical p-energy measures for strongly local p-energy forms, proves chain/Leibniz rules and uniqueness, and shows coincidence with Korevaar-Schoen-type measures via a p-analogue of Le Jan's domination principle.
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Cartesian products of Sierpi\'nski carpets do not attain their conformal dimension
Cartesian products of the Sierpiński carpet (and similar self-similar fractals) with itself at least twice do not attain their conformal dimension.
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Sobolev spaces on snowtrees
On Ahlfors-regular ε-snowtrees the discrete-energy Sobolev space equals the Korevaar–Schoen space for every multiscale partition, with critical exponent α_p = Q/p + 1/ε − 1/(pε).
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Construction of $p$-energy measures associated with strongly local $p$-energy forms
Constructs canonical p-energy measures for strongly local p-energy forms, proves chain/Leibniz rules and uniqueness, and shows coincidence with Korevaar-Schoen-type measures via a p-analogue of Le Jan's domination principle.
- Iterated Graph Systems (I): random walks and diffusion limits