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- Thread starter dwsmith
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How would that be used? An open disc doesn't have a maximum modulus.Did you try by contradiction, using the maximum modulus principle?

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- #5

That still doesn't make sense. Every time we get close to the boundary, we can get a little bit closer. Moreover, we can get a little bit closer and infinite amount of times.Use the fact that the maximum of the modulus is reached at the boundary.

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- #7

I don't understand what you are getting at.In fact, we have to work with the map $M(r):=\sup_{|z|=r}|f(z)|$. We can show thanks to maximum modulus principle that this map is strictly increasing.