---
tag: Q5C1E10CSQ
kind: concept
name: H-cone
msc: [31D05]
sources:
  - url: https://en.wikipedia.org/wiki/Potential_theory
---

## Summary

An H-cone is an ordered convex cone whose axioms abstract the properties of the cone of positive [[superharmonic functions|X4V2S56YQQ]] on a domain.
The theory of H-cones was developed by Nicu Boboc, Gheorghe Bucur and Aurel Cornea.
It treats potential theory as the study of an ordered cone, with no underlying space of points given in advance.
Under further conditions an H-cone can be represented as a cone of functions on a suitable space.

## Explanations

### L1 human

Positive superharmonic functions can be added, multiplied by positive numbers, and compared, and they form a cone with a rich order structure.
Many results of potential theory, such as balayage and the decomposition of a function into a potential and a harmonic part, depend mainly on this structure.
An H-cone is a cone with these order properties, taken as axioms.
In this way one theory applies at once to harmonic spaces, to Markov processes and to other settings.