Extremal Properties of Quasiharmonic Forms and Functions.

摘要

The purpose of the present paper is to deduce extremal properties of differential forms phi satisfying the differential equations (delta)dT phi + PT(phi) = 0 or (delta)dT(phi) + d(delta)S(phi) = 0 on a space. For suitable choices of the operators T and S and the nonnegative function P the authors obtain, in a unified manner, extremal properties of harmonic, semiharmonic, cosemiharmonic, quasiharmonic, and coquasiharmonic forms, and harmonic, P-harmonic, quasiharmonic, and P-quasiharmonic functions. (Author)