Plane harmonic measures live on sets of \(\sigma\)-finite length

DOI10.1007/BF02559503zbMath0809.30007OpenAlexW2047945094MaRDI QIDQ1312330

Thomas H. Wolff

Publication date: 28 March 1995

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02559503

zbMATH Keywords

capacityharmonic measureHausdorff measure

Mathematics Subject Classification ID

General theory of conformal mappings (30C35) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (10)

Applications of Boundary Harnack Inequalities for p Harmonic Functions and Related Topics ⋮ Bernoulli type free boundary problems and water waves ⋮ Unavoidable sets and harmonic measures living on small sets ⋮ Hausdorff dimension and \(\sigma\) finiteness of \(p\) harmonic measures in space when \(p \geq n\) ⋮ \(p\) harmonic measure in simply connected domains ⋮ Absolute continuity of harmonic measure for domains with lower regular boundaries ⋮ \(\sigma\)-finiteness of elliptic measures for quasilinear elliptic PDE in space ⋮ Regularity of optimal shapes for the Dirichlet's energy with volume constraint ⋮ 𝑝 harmonic measure in simply connected domains revisited ⋮ Hausdorff dimension of harmonic measure for self-conformal sets

Cites Work

• On conformal mapping and linear measure
• Hausdorff dimension of harmonic measures in the plane
• On the Distortion of Boundary Sets Under Conformal Mappings
• On the support of harmonic measure for sets of Cantor type
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