Revista Matemática Iberoamericana· 2026Q1
The Hausdorff dimension of planar elliptic measures via quasiconformal mappings
- 1citations
- Q1SCImago
- 2026year
Short summary
New bounds for the Hausdorff dimension of planar elliptic measures are derived using quasiconformal mappings, depending only on the ellipticity constant.
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Key points
- New bounds for Hausdorff dimension of planar elliptic measures are established.
- Bounds depend exclusively on the ellipticity constant of the matrix.
- Quasiconformal mappings are used to relate elliptic and harmonic measures.
- Results extend previous work by Makarov, Jones, and Wolff.
AI-generated from the title and abstract; the full text is not read.
Abstract
In this paper, we obtain new bounds for the Hausdorff dimension of planar elliptic measure via the application of quasiconformal mappings, with these bounds depending solely on the ellipticity constant of the matrix. In fact, in our case studies, we find a quasiconformal mapping that relates the elliptic measure in a domain to the harmonic measure in its image domain, allowing us to deduce bounds for the dimension of the elliptic measure from the known results on the harmonic side. This extends previous works of Makarov, Jones and Wolff.
The authors' abstract, as published at the source. Revista Matemática Iberoamericana, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics