Geodesic
Potential theory in the class of $m$-subharmonic functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 166-192

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A potential theory for the equation $(dd^\mathrm cu)^m\wedge\beta^{n-m}=f\beta^n$, $1\le m\le n$, is developed. The corresponding notions of $m$-capacity and $m$-subharmonic functions are introduced, and their properties are studied. 
@article{TM_2012_279_a10,
     author = {A. Sadullaev and B. Abdullaev},
     title = {Potential theory in the class of $m$-subharmonic functions},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {166--192},
     publisher = {mathdoc},
     volume = {279},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_279_a10/}
}
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A. Sadullaev; B. Abdullaev. Potential theory in the class of $m$-subharmonic functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 166-192. http://geodesic.mathdoc.fr/item/TM_2012_279_a10/