Potential theory Harmonic functions Concept
Harmonic measure
Summary
The harmonic measure of a domain, seen from a point , is a probability measure on the boundary of the domain. It is the measure that represents the value at of the solution of the Dirichlet problem in terms of the boundary data. Equivalently, it is the distribution of the first exit point of a Brownian motion started at . It is invariant under conformal maps, and it is a central tool for estimating harmonic and holomorphic functions near the boundary.
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About this page
| Tag | CFD7BPM51W |
|---|---|
| URI | m2://CFD7BPM51W |
| Kind | concept |
| Writing | W0 stub |
| MSC | 31A15, 30C85 |
| Same as |
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Used by
- Balayage
- Mutual absolute continuity of harmonic measures
- Makarov's theorem on harmonic measure
- Beurling's projection theorem
- Dahlberg's theorem on harmonic measure
- Bourgain's dimension bound for harmonic measure
- Harmonic measure as exit distribution
- Hadamard's two-constants theorem
Results about this
- Mutual absolute continuity of harmonic measures
- Makarov's theorem on harmonic measure
- Beurling's projection theorem
- Dahlberg's theorem on harmonic measure
- Bourgain's dimension bound for harmonic measure
- Harmonic measure as exit distribution
- Hadamard's two-constants theorem