Geodesic
Stability and Continuity of Functions of Least Gradient
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1
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In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop some stability properties of sequences of least gradient functions. We also apply these tools to prove a maximum principle for functions of least gradient that arise as solutions to a Dirichlet problem.
Mots-clés : least gradient, BV; metric measure spac, approximate continuity, continuity, stability, jump set, Dirichlet problem, minimal surface 
@article{AGMS_2015_3_1_a15,
     author = {Hakkarainen, H. and Korte, R. and Lahti, P. and Shanmugalingam, N.},
     title = {Stability and {Continuity} of {Functions} of {Least} {Gradient}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2015},
     volume = {3},
     number = {1},
     zbl = {1318.26028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a15/}
}
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Hakkarainen, H.; Korte, R.; Lahti, P.; Shanmugalingam, N. Stability and Continuity of Functions of Least Gradient. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a15/