Dimension of quasicircles

By Stanislav Smirnov. 2009

59 citations recorded by the source corpus.

We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala’s conjecture that the Hausdorff dimension of a k-quasicircle is at most 1+k2.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/10c49f98236e46d540855aa7cad62a401691e690

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In Applied Mathematics

1. A. Ukhlov
2. V. Gol’dshtein

In Geometry and Topology

1. A. Ukhlov
2. V. Gol’dshtein

In Mathematical Physics

1. A. Ukhlov
2. V. Gol’dshtein

Citations in the corpus

• On the First Eigenvalues of Free Vibrating Membranes in Conformal Regular Domains (2015, background): “Smirnov proved recently [30] that the Hausdorff dimension of any K-quasicircle is at most 1 + k(2), where k = (K − 1)/(K + 1).”