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• W2896537259 abstract "In this paper, we study the asymptotic behavior of BV functions in complete metric measure spaces equipped with a doubling measure supporting a $1$-Poincare inequality. We show that at almost every point $x$ outside the Cantor and jump parts of a BV function, the asymptotic limit of the function is a Lipschitz continuous function of least gradient on a tangent space to the metric space based at $x$. We also show that, at co-dimension $1$ Hausdorff measure almost every measure-theoretic boundary point of a set $E$ of finite perimeter, there is an asymptotic limit set $(E)_infty$ corresponding to the asymptotic expansion of $E$ and that every such asymptotic limit $(E)_infty$ is a quasiminimal set of finite perimeter. We also show that the perimeter measure of $(E)_infty$ is Ahlfors co-dimension $1$ regular." @default.
• W2896537259 created "2018-10-26" @default.
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• W2896537259 date "2018-10-12" @default.
• W2896537259 modified "2023-09-27" @default.
• W2896537259 title "Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spaces" @default.
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