Fat sets and pointwise boundary estimates forp-harmonic functions in metric spaces

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Lebesgue points for Sobolev functions on metric spaces (2002, unknown): “The result has applications to the regularity theory for minimizers of variational integrals on metric measure spaces, see [2].”
Modulus and the Poincaré inequality on metric measure spaces (2003, background): “This has been extensively studied, see [HKM93,HK95a,HK96,HK98,HK99, BMS01 ,HST01,Sha01, HKST01,KST01,Kei02].”
Obstacle and Dirichlet problems on arbitrary nonopen sets in metric spaces, and fine topology (2012, methodology): “sition 3.10, gu= gu,E in this case (if Eis measurable). The variational capacity capp(A,E) has been used and studied earlier on metric spaces for bounded open E in e.g. Bj¨orn–MacManus–Shanmugalingam [13] and J. Bj¨orn [11]. It can also be regarded as the condenser capacity capp(X\E,A,X), as in Deﬁn”
The Poincare inequality is an open ended condition (2008, methodology): “[2] J. Björn, P. MacManus, and N. Shanmugalingam, Fat sets and pointwise boundary estimates for p-harmonic functions in metric spaces, J. Anal.”
Geometric Implications of the Poincaré Inequality (2007, background): “In [ 4 ] and [11] the standing assumption is that the space is locally linearly connecdted”