Explore: Subharmonic Functions

theory. Intuitively, subharmonic functions are related to convex functions of one variable as follows. If the graph of a convex function and a line intersect

hold, although other properties of harmonic functions may fail. More generally, a function is subharmonic if and only if, in the interior of any ball

discrete Laplace operator. Similar to continuous subharmonic functions one can define subharmonic functions for finite-difference approximations u h {\displaystyle

Kähler manifold, plurisubharmonic functions form a subset of the subharmonic functions. However, unlike subharmonic functions (which are defined on a Riemannian

sets), convex functions (on vector and affine spaces), harmonic and subharmonic functions (on Riemannian manifolds), analytic functions (usually of one

potential theory, a subharmonic function f satisfies Δf ≥ 0. Any subharmonic function that is bounded above by a harmonic function for all points on the

in which he gave a solution to Plateau's problem, and in 1935, "Subharmonic Functions". His work focused on computer science in the last decade of his

natural topology for setting the study of subharmonic functions. In the earliest studies of subharmonic functions, namely those for which Δ u ≥ 0 , {\displaystyle

used in the proof of the Choquet theorem. Similar ideas applied to subharmonic functions are used in the Perron method for solving the Dirichlet problem

whether function spaces other than the negative subharmonic functions are degenerate, e.g. Riemann surfaces on which all bounded holomorphic functions are