Peak function

Summary

A peak function at a boundary point $p$ of a domain is a holomorphic function, continuous up to the boundary, that equals $1$ at $p$. At every other point of the closure its modulus is less than $1$. A point with a peak function is a peak point. Peak functions help to localize problems at the boundary and to show that a domain is a domain of holomorphy. They are also used to study the boundary behaviour of holomorphic maps.