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- W2048405280 abstract "Let $D subsetneqq mathbf {C}$ and $Delta subsetneqq mathbf {C}$ be open sets in the plane $mathbf {C}$ containing 0. Suppose that $D$ is connected and $f$ is holomorphic in $D$ with $f(0) = 0$. Then, for $Q = f(D) cap Delta$ and $P = {f^{ - 1}}(Q)$, we have [ A(P) + A(Q) geqslant pi {[min { operatorname {dis}(partial D,0),operatorname {dis}(partial Delta ,0)} ]^2},] $A( cdot )$ denoting the area. The constant $pi$ is sharp and the equality holds if and only if $f equiv 0,operatorname {dis}(partial D,0) leqslant operatorname {dis}(partial Delta ,0)$, and $D$ is a disk of center 0." @default.
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- W2048405280 date "1985-04-01" @default.
- W2048405280 modified "2023-10-14" @default.
- W2048405280 title "An area theorem for holomorphic functions" @default.
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- W2048405280 doi "https://doi.org/10.1090/s0002-9939-1985-0776189-3" @default.
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