The existence theorem of harmonic objects via Green function (Q2752834)

For a given non-compact Riemannian manifold \(M\) endowed with a positive Green function, it is known that a smooth function \(f_0\) with a suitable growth condition imposed on its Laplacian provides in a standard way a harmonic function \(f\) on \(M\) having the same boundary conditions as \(f_0\). The author shows that this method can be applied to prove existence theorems of differential geometric objects of harmonic type.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00035].