We describe some aspects of potential theory on Riemannian manifolds, concentrating on Liouville-type theorems and their relationships with the parabolicity and stochastic completeness of the underlying manifold. Some generalizations of these concepts to the case of non-linear operators are also discussed.
Pigola, S., Rigoli, M., Setti, A. (2008). Aspects of potential theory on manifolds, linear and non-linear. MILAN JOURNAL OF MATHEMATICS, 76(1), 229-256 [10.1007/s00032-008-0084-1].
Aspects of potential theory on manifolds, linear and non-linear
Pigola S.
;
2008
Abstract
We describe some aspects of potential theory on Riemannian manifolds, concentrating on Liouville-type theorems and their relationships with the parabolicity and stochastic completeness of the underlying manifold. Some generalizations of these concepts to the case of non-linear operators are also discussed.
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