Annales Academić Scientiarum Fennicć
Mathematica
Volumen 33, 2008, 205-230

EUCLIDEAN QUASICONVEXITY

Hrant Hakobyan and David A. Herron

Stony Brook University, Department of Mathematics
Stony Brook, NY 11794-3651, U.S.A.; hhakob 'at' math.sunysb.edu

University of Cincinnati, Department of Mathematical Sciences
839 Old Chemistry Building, Cincinnati, OH 45221-0025, U.S.A.; David.Herron 'at' math.UC.edu

Abstract. We exhibit compact totally disconnected sets in Rⁿ, with Hausdorff dimension n - 1, whose complements fail to be quasiconvex, and similar sets with positive n-measure whose complements are quasiconvex. We characterize the finitely connected quasiconvex plane domains. We present related results for bounded turning.

2000 Mathematics Subject Classification: Primary 30C655; Secondary 51F99.

Key words: Quasiconvex, Jordan curve, Hausdorff dimension.

Reference to this article: H. Hakobyan and D.A. Herron: Euclidean quasiconvexity. Ann. Acad. Sci. Fenn. Math. 33 (2008), 205-230.

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