Relative isoperimetric inequalities and sufficient conditions for finite perimeter on metric spaces

Aalto, 2010, The discrete maximal operator in metric spaces, J. Anal. Math., 111, 369, 10.1007/s11854-010-0022-3 Ambrosio, 2002, Fine properties of sets of finite perimeter in doubling metric measure spaces, Set-Valued Anal., 10, 111, 10.1023/A:1016548402502 Ambrosio, 2000, Functions of Bounded Variation and Free Discontinuity Problems Ambrosio, 2004, Special functions of bounded variation in doubling metric measure spaces, vol. 14, 1 Ambrosio, 2004, Topics on Analysis in Metric Spaces, vol. 25 Björn, 2011, Nonlinear Potential Theory on Metric Spaces, vol. 17 Björn, 2008, Quasicontinuity of Newton–Sobolev functions and density of Lipschitz functions on metric spaces, Houston J. Math., 34, 1197 Bobkov, 1997, Some connections between isoperimetric and Sobolev-type inequalities, Mem. Amer. Math. Soc., 129 Buckley, 1999, Is the maximal function of a Lipschitz function continuous?, Ann. Acad. Sci. Fenn. Math., 24, 519 C.S. Camfield, Comparison of BV norms in weighted Euclidean spaces and metric measure spaces, PhD thesis, University of Cincinnati, 2008. Cheeger, 1999, Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal., 9, 428, 10.1007/s000390050094 Csörnyei, 2012, Points of middle density in the real line, Real Anal. Exchange, 37, 243, 10.14321/realanalexch.37.2.0243 Evans, 1992, Measure Theory and Fine Properties of Functions Federer, 1969, Geometric Measure Theory, vol. 153 Giusti, 1984, Minimal Surfaces and Functions of Bounded Variation, vol. 80 Hajłasz, 2003, Sobolev spaces on metric-measure spaces, vol. 338, 173 Hajłasz, 2000, Sobolev met Poincaré, Mem. Amer. Math. Soc., 145 Hakkarainen, 2010, The BV-capacity in metric spaces, Manuscripta Math., 132, 51, 10.1007/s00229-010-0337-5 Hakkarainen, 2011, Comparisons of relative BV-capacities and Sobolev capacity in metric spaces, Nonlinear Anal., 74, 5525, 10.1016/j.na.2011.05.036 Heinonen, 2001, Lectures on Analysis on Metric Spaces, 10.1007/978-1-4613-0131-8 Heinonen, 1998, Quasiconformal maps in metric spaces with controlled geometry, Acta Math., 181, 1, 10.1007/BF02392747 Järvenpää, 2007, Measurability of equivalence classes and MECp-property in metric spaces, Rev. Mat. Iberoam., 23, 811, 10.4171/RMI/514 Keith, 2003, Modulus and the Poincaré inequality on metric measure spaces, Math. Z., 245, 255, 10.1007/s00209-003-0542-y Kinnunen, 2008, Characterizations of Sobolev inequalities on metric spaces, J. Math. Anal. Appl., 344, 1093, 10.1016/j.jmaa.2008.03.070 Kinnunen, 2008, Lebesgue points and capacities via the boxing inequality in metric spaces, Indiana Univ. Math. J., 57, 401, 10.1512/iumj.2008.57.3168 Kinnunen, 2012, A characterization of Newtonian functions with zero boundary values, Calc. Var. Partial Differential Equations, 43, 507, 10.1007/s00526-011-0420-0 J. Kinnunen, R. Korte, N. Shanmugalingam, H. Tuominen, Pointwise properties of functions of bounded variation in metric spaces, preprint, 2011. Korte, 2007, Geometric implications of the Poincaré inequality, Results Math., 50, 93, 10.1007/s00025-006-0237-x Kurka, 2011, Optimal quality of exceptional points for the Lebesgue density theorem, Acta Math. Hungar., 134, 209, 10.1007/s10474-011-0182-3 Lahti Miranda, 2003, Functions of bounded variation on “good” metric spaces, J. Math. Pures Appl. (9), 82, 975, 10.1016/S0021-7824(03)00036-9 Shanmugalingam, 2000, Newtonian spaces: an extension of Sobolev spaces to metric measure spaces, Rev. Mat. Iberoam., 16, 243, 10.4171/RMI/275 Szenes, 2011, Exceptional points for Lebesgue's density theorem on the real line, Adv. Math., 226, 764, 10.1016/j.aim.2010.07.011 Ziemer, 1989, Weakly Differentiable Functions, vol. 120