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Domains with growth conditions for the quasihyperbolic metric

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Abstract

For a given growth functionH, we say that a domainD ⊂R n is anH-domain if δD x≤δD(x 0)H(k D(x,x 0)),x ∈D, where δD(x)=d(x∂D) andk D denotes the quasihyperbolic distance. We show that ifH satisfiesH(0)=1, |H'|≤H, andH"≤H, then there exists an extremalH-domain. Using this fact, we investigate some fundamental properties ofH-domains.

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Authors and Affiliations

  1. Department of Mathematics, National Defense Academy, Hashirimizu-1-10-20, 239, Yokosuka, Japan

    Yasuhiro Gotoh

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  1. Yasuhiro Gotoh
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Correspondence to Yasuhiro Gotoh.

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Dedicated to Professor Masayuki Itô on his sixtieth birthday

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Gotoh, Y. Domains with growth conditions for the quasihyperbolic metric. J. Anal. Math. 82, 149–173 (2000). https://doi.org/10.1007/BF02791225

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  • DOI: https://doi.org/10.1007/BF02791225

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