Aspects of potential theory on manifolds, linear and non-linear
The authors describe some aspects of potential theory on Riemannian manifolds, concentrating on Liuoville-type theorems and their relationships with parabolicity and stochastic completeness of the underlying manifold. The paper starts with an overview of parabolicity, then goes into the relationship between stochastic completeness and the weak maximum principle, and then some possible generalizations of these concepts to the case of nonlinear operators such as the \(\phi\)-Laplacian with \(\phi\) satisfying certain conditions. Particular attention is paid to the \(p\)-Laplacian, \(p>1\), which is a special case of the \(\phi\)-Laplacian with \(\phi(t)=t^{p-1}\).
scientific article; zbMATH DE number 5624126