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Sep 28, 2019 at 18:56 history edited Anthony Quas CC BY-SA 4.0
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Sep 28, 2019 at 18:20 comment added Anthony Quas Take $z’=e^{i(\theta’-\theta)z}$
Sep 28, 2019 at 11:12 comment added ray I am not yet convinced. In fact, since the argument of $z$ may be far away from $\theta$, I do not yet see why this $z'$ in the other cone and close to $z$ should exist. The whole must somehow use the relation $|\arg z-\theta|< C (1-|z|)$ between the argument of $z$ and $\theta$ (so also with $\theta'$) which comes from the hypothesis that $z$ belongs to a cone with endpoint $e^{i\theta}$.
Sep 28, 2019 at 3:03 history edited Anthony Quas CC BY-SA 4.0
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Sep 28, 2019 at 2:52 history edited Anthony Quas CC BY-SA 4.0
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Sep 27, 2019 at 18:31 comment added ray Could you please give us some hints why this maximum function is continuous? (there may be whole arcs on where the maximum is taken).
Sep 27, 2019 at 2:24 history answered Anthony Quas CC BY-SA 4.0