## Advanced Studies in Pure Mathematics

### On the behavior at infinity for non-negative superharmonic functions in a cone

Minoru Yanagishita

#### Abstract

This paper shows that a positive superharmonic function on a cone behaves regularly outside an $\alpha$-minimally thin set in a cone. This fact is known for a half space which is a special cone.

#### Article information

Dates
Revised: 1 December 2005
First available in Project Euclid: 16 December 2018

https://projecteuclid.org/ euclid.aspm/1544999707

Digital Object Identifier
doi:10.2969/aspm/04410403

Mathematical Reviews number (MathSciNet)
MR2279772

Zentralblatt MATH identifier
1116.31002

Subjects
Primary: 31B05: Harmonic, subharmonic, superharmonic functions
Secondary: 31B20: Boundary value and inverse problems

#### Citation

Yanagishita, Minoru. On the behavior at infinity for non-negative superharmonic functions in a cone. Potential Theory in Matsue, 403--413, Mathematical Society of Japan, Tokyo, Japan, 2006. doi:10.2969/aspm/04410403. https://projecteuclid.org/euclid.aspm/1544999707