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  "body": "\n## Summary\n\nA peak function at a boundary point $p$ of a domain is a holomorphic function, continuous up to the boundary, that equals $1$ at $p$.\nAt every other point of the closure its modulus is less than $1$.\nA point with a peak function is a peak point.\nPeak functions help to localize problems at the boundary and to show that a domain is a domain of holomorphy.\nThey are also used to study the boundary behaviour of holomorphic maps.\n\n## Explanations\n\n### L1 human\n\nA peak function is a holomorphic function whose modulus has a single highest point on the closed domain, and that point is on the boundary.\nPowers $f^k$ of a peak function $f$ are then close to $1$ near $p$ and close to $0$ away from $p$, so they act like holomorphic \"spotlights\" on $p$.\nOn the closed unit disc, $f(z) = (1 + z)/2$ peaks at $z = 1$.\nOn the bidisc, the boundary points $(1, b)$ with $\\abs{b} \u003c 1$ have no peak function, because the boundary contains a flat disc through them.\n",
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