Superharmonic functions on foliations

S. R. Adams
1992 Transactions of the American Mathematical Society  
We use techniques from geometric analysis to prove that any positive, leafwise superharmonic, measurable function on a Riemannian measurable foliation with transverse invariant measure, finite total volume and complete leaves is, in fact, constant on a.e. leaf.
doi:10.1090/s0002-9947-1992-1033232-2 fatcat:d27iwtbejvbm7nzuhvqsxac5x4