 If "ƒ""t" is a suitable normalized isomorphism from "D" to "D""t", then it satisfies a differential equation found by in his work on the Bieberbach conjecture.Sometimes it is more convenient to use the inverse function "g""t" of "ƒ""t", which is a conformal mapping from "D""t" to "D".In Loewner's equation, "z" is in the domain "D", "t" ≥ 0, and the boundary values at time "t" = 0 are "ƒ"0("z") = "z" or "g"0("z") = "z".