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- W3020556295 abstract "We show that the inner distance inside a bounded planar domain is at most the one-dimensional Hausdorff measure of the boundary of the domain. We prove this sharp result by establishing an improved Painleve length estimate for connected sets and by using the metric removability of totally disconnected sets, proven by Kalmykov, Kovalev, and Rajala. We also give a totally disconnected example showing that for general sets the Painleve length bound $kappa(E) lepi mathcal{H}^1(E)$ is sharp." @default.
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- W3020556295 date "2020-01-01" @default.
- W3020556295 modified "2023-09-24" @default.
- W3020556295 title "Sharp estimate on the inner distance in planar domains" @default.
- W3020556295 doi "https://doi.org/10.4310/arkiv.2020.v58.n1.a9" @default.
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