The Dirichlet problem for a disk on the sphere \(S^2\)
The author obtains the solution of the Dirichlet problem for circular disks on the two-dimensional Euclidean sphere by taking the average of certain weighted means of the boundary function over all chords through a given point. A similar problem was already solved in the case of the Euclidean and hyperbolic plane.
scientific article; zbMATH DE number 1394886