Hausdorff dimension of harmonic measures in the plane
From MaRDI portal
Publication:1117345
DOI10.1007/BF02392296zbMath0667.30020OpenAlexW2084462739MaRDI QIDQ1117345
Peter W. Jones, Thomas H. Wolff
Publication date: 1988
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02392296
Capacity and harmonic measure in the complex plane (30C85) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)
Related Items
Dissipation in weakly polarizable electrodes across irregular boundaries ⋮ Applications of Boundary Harnack Inequalities for p Harmonic Functions and Related Topics ⋮ Rectifiability of harmonic measure ⋮ A Discrete Analogue of a Theorem of Makarov ⋮ Capacity and principal eigenvalues: The method of enlargement of obstacles revisited ⋮ Fine structure of connectedness loci ⋮ Unavoidable sets and harmonic measures living on small sets ⋮ On the dimension of \(p\)-harmonic measure in space ⋮ Harmonic measure and polynomial Julia sets ⋮ Cantor sets with absolutely continuous harmonic measure ⋮ On the exit distribution of partially reflected Brownian motion in planar domains ⋮ Hausdorff dimension and \(\sigma\) finiteness of \(p\) harmonic measures in space when \(p \geq n\) ⋮ Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension-one Hausdorff measure ⋮ Dimension drop for harmonic measure on Ahlfors regular boundaries ⋮ \(p\) harmonic measure in simply connected domains ⋮ Dahlberg's theorem in higher co-dimension ⋮ \(\sigma\)-finiteness of elliptic measures for quasilinear elliptic PDE in space ⋮ Integrability of Superharmonic Functions and Subharmonic Functions ⋮ Where does a random process hit a fractal barrier? ⋮ Harmonic measure of the planar Cantor set from the viewpoint of graph theory ⋮ Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions ⋮ 𝑝 harmonic measure in simply connected domains revisited ⋮ Plane harmonic measures live on sets of \(\sigma\)-finite length ⋮ Harmonic measure of the outer boundary of colander sets ⋮ A characterization of Poissonian domains ⋮ On the Riesz charge of the lower envelope of \(\delta\)-subharmonic functions.
Cites Work
- Unnamed Item
- The dimension of the maximal measure for a polynomial map
- Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map
- On the snow flake domain
- Critical points of Green's function, harmonic measure, and the corona problem
- Can one hear the dimension of a fractal?
- Negatively curved manifolds, elliptic operators, and the Martin boundary
- Brownian motion and sets of harmonic measure zero
- On the Hausdorff dimension of harmonic measure in higher dimension
- On the Distortion of Boundary Sets Under Conformal Mappings
- On the support of harmonic measure for sets of Cantor type
- Null Sets for Measures Orthogonal to R(X)
