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Strong approximation of sets of finite perimeter in metric spaces (1611.06162v1)

Published 18 Nov 2016 in math.MG

Abstract: In the setting of a metric space equipped with a doubling measure that supports a Poincar\'e inequality, we show that any set of finite perimeter can be approximated in the BV norm by a set whose topological and measure theoretic boundaries almost coincide. This result appears to be new even in the Euclidean setting. The work relies on a quasicontinuity-type result for BV functions proved by Lahti and Shanmugalingam (2016).

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