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