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math.MG2023★ 1 cited
First-order Sobolev spaces, self-similar energies and energy measures on the Sierpiński carpet
Mathav Murugan, Ryosuke Shimizu
We construct and investigate -Sobolev space, -energy, and the corresponding -energy measures on the planar Sierpiński carpet for all . Our method i…
math.MG2022
Conformal Assouad dimension as the critical exponent for combinatorial modulus
Mathav Murugan
The conformal Assouad dimension is the infimum of all possible values of Assouad dimension after a quasisymmetric change of metric. We show that the conformal Assouad dimension equ…