On some Liouville theorems on noncompact Riemannian manifolds
The author considers the problem of existence of bounded harmonic functions, i.e., solutions to the equation \(\Delta u =0\) on noncompact manifolds where \(\Delta\) is the Laplace-Beltrami operator. For manifolds which look at infinity like a product of Riemannian manifolds and a line, a criterion for the existence of such functions is given. This criterion is also generalized for the existence of bounded solutions to the equation \(\Delta u = c u\) on the same manifolds.
scientific article; zbMATH DE number 1431738