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.
Aspects of potential theory on manifolds, linear and non-linear / S. Pigola, M. Rigoli, A.G. Setti. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - 76:1(2008), pp. 229-256.
Aspects of potential theory on manifolds, linear and non-linear
M. RigoliSecondo
;
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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