The area of the unit disk under a holomorphic function

Asked Jun 02 '19 at 11:21

Active Jun 02 '19 at 11:21

Viewed 247 times

Suppose that $f:D\to\mathbb C$ is a holomorphic function, where $D$ is the unit disk, and $f'(0)=1$. How can I prove that the area of $f(D)$ is no less than $\pi$?

The case that $f$ is injective is easy, because in this case the area of $f(D)$ can be expressed by the coeffecients of the Taylor series of $f$ at $0$, but how about the case that $f$ is not injective?

Thanks in advance!

asked Jun 02 '19 at 11:21

Frank Kong

1

https://math.stackexchange.com/questions/828846/the-area-of-the-image-under-a-specific-holomorphic-function-of-the-unit-disk – logo Jun 02 '19 at 11:37
Is there any reason to expect this to be true in the noninjective case? – Carlos Esparza Dec 11 '20 at 02:50

The area of the unit disk under a holomorphic function

0 Answers0