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Geometric Implications of the Poincaré Inequality

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Abstract.

The purpose of this work is to prove the following result: If a doubling metric measure space supports a weak (1, p)–Poincaré inequality with p sufficiently small, then annuli are almost quasiconvex. We also obtain estimates for the Hausdorff s-content and the diameter of the spheres.

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  1. Institute of Mathematics, Helsinki University of Technology, P.O.Box 1100, FIN-02015, Helsinki, Finland

    Riikka Korte

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  1. Riikka Korte
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Correspondence to Riikka Korte.

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Submitted: April 18, 2006.

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Korte, R. Geometric Implications of the Poincaré Inequality. Result. Math. 50, 93–107 (2007). https://doi.org/10.1007/s00025-006-0237-x

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  • DOI: https://doi.org/10.1007/s00025-006-0237-x

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