Sharp Hausdorff content estimates for accessible boundaries of domains in metric measure spaces of controlled geometry
Eriksson-Bique, S., Gibara, R., Korte, R., & Shanmugalingam, N. (2024). Sharp Hausdorff content estimates for accessible boundaries of domains in metric measure spaces of controlled geometry. Transactions of the American Mathematical Society : Series B, 11, 1435-1461. https://doi.org/10.1090/btran/210
Date
2024Copyright
© 2024 by the author(s)
We give a sharp Hausdorff content estimate for the size of the accessible boundary of any domain in a metric measure space of controlled geometry, i.e., a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality for a fixed 1 ≤ p < ∞. This answers a question posed by Jonas Azzam. In the process, we extend the result to every doubling gauge in metric measure spaces which satisfies a codimension one bound.
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American Mathematical SocietyISSN Search the Publication Forum
2330-0000Keywords
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https://converis.jyu.fi/converis/portal/detail/Publication/245031821
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Research Council of FinlandFunding program(s)
Postdoctoral Researcher, AoF; Academy Research Fellow, AoFAdditional information about funding
The fourth author’s work was partially supported by the NSF (U.S.A.) grant DMS #2054960. The first author’s work was partially supported by the Finnish Academy grants no. 356861 and 35424.License
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