Partial Balayage on Riemannian Manifolds
(English)Manuscript (preprint) (Other academic)
A general theory of partial balayage on Riemannian manifolds is developed, with emphasis on compact manifolds. Partial balayage is an operation of sweeping measures, or charge distributions, to a prescribed density, and it is closely related to (construction of) quadrature domains for subharmonic functions, growth processes such as Laplacian growth and to weighted equilibrium distributions.
Several examples are given in the paper, as well as some specific results. For instance, it is proved that, in two dimensions, harmonic and geodesic balls are the same if and only if the Gaussian curvature of the manifold is constant.
Partial balayage, Riemannian manifold, equilibrium measure, quadrature domain, Laplacian growth, harmonic ball, obstacle problem, complementarity problem
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-186346OAI: oai:DiVA.org:kth-186346DiVA: diva2:927044
QC 201605252016-05-102016-05-102016-05-25Bibliographically approved