Geodesic
A new characterization of chord-arc domains
Journal of the European Mathematical Society, Tome 19 (2017) no. 4, pp. 967-981 Cet article a éte moissonné depuis la source EMS Press

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We show that if Ω⊂Rn+1, n≥1, is a uniform domain (also known as a 1-sided NTA domain), i.e., a domain which enjoys interior Corkscrew and Harnack Chain conditions, then uniform rectifiability of the boundary of Ω implies the existence of exterior corkscrew points at all scales, so that in fact, Ω is a chord-arc domain, i.e., a domain with an Ahlfors-David regular boundary which satisfies both interior and exterior corkscrew conditions, and an interior Harnack chain condition. We discuss some implications of this result for theorems of F. and M. Riesz type, and for certain free boundary problems.
DOI : 10.4171/jems/685
Classification : 28-XX, 31-XX, 35-XX, 42-XX
Keywords: Chord-arc domains, NTA domains, 1-sided NTA domains, uniform domains, uniform rectifiability, Carleson measures, harmonic measure, A∞​ Muckenhoupt weights 
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     author = {Jonas Azzam and Steve Hofmann and Jos\'e Mar{\'\i}a Martell and Kaj Nystr\"om and Tatiana Toro},
     title = {A new characterization of chord-arc domains},
     journal = {Journal of the European Mathematical Society},
     pages = {967--981},
     year = {2017},
     volume = {19},
     number = {4},
     doi = {10.4171/jems/685},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/685/}
}
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Jonas Azzam; Steve Hofmann; José María Martell; Kaj Nyström; Tatiana Toro. A new characterization of chord-arc domains. Journal of the European Mathematical Society, Tome 19 (2017) no. 4, pp. 967-981. doi: 10.4171/jems/685

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