Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a p-Poincaré inequality

2023/08/18 by Eriksson-Bique, Sylvester, Gibara, Ryan, Korte, Riikka +1
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2308.09800

Abstract

We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "visibility" indicates the existence of John curves connecting the interior point to the points on the "visible boundary". In this paper, we provide an affirmative answer in the setting of a doubling metric measure space supporting a p-Poincaré inequality for 1

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