●Introduction
Chapter 1.Motivation and statement of the main results
1.Characterization (1)α: Approximation with planes
2.Characterization (2)α: Introducing BMO and VMO
3. ltiplicative vs.additive formulation: Introducing the doubling condition
4.Characterization (1)α and flatness
5.Doubling and asymptotically optimally doubling measures
6.Regularity of a domain and doubling character of its harmonic measure
7.Regularity of a domain and smoothness of its Poisson kernel
Chapter 2.The relation between potential theory and geometry for planar domains
1.Smooth domains
2.Non smooth domains
3.Preliminaries to the proofs of Theorems 2.7 and 2.8
4.Proof of Theorem 2.7
5.Proof of Theorem 2.8
6.Notes
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