An extremal problem for Dirichlet-finite holomorphic functions on Riemann surfaces |
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| Authors: | Shinji Yamashita |
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| Institution: | (1) Department of Mathematics, Tokyo Metropolitan University, Fukasawa, Setagaya, 158 Tokyo, Japan |
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| Abstract: | Iff is a nonconstant holomorphic function with finite Dirichlet integralD(f) on a Riemann surfaceR, then |f|2 has the least harmonic majorantf
2 onR. We show Σf
2(a ≦π
−1
D(f)), wherea runs over all the roots off = 0 onR. The equality holds if and only iff is of type ℬℓ1 fromR onto a disk of center 0. A consideration is proposed for the non-Euclidean case. |
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| Keywords: | |
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