Re: subharmonic functions in the plane

On 6 Apr 2007 14:12:26 -0700, "martyfin" <marty0801@xxxxxxxxxxx>
wrote:

I want to prove the following uniqueness theorem for subharmonic
functions in the complex plane:

Let D be a neighborhood of infinity, simpliconnected in the closed
complex plane, and u a nonegative subharmonic function on D which
vanishes at a fixed point x in D and at infinity. Then u=0 in D.

Is it true?

If my guess regarding what it means for a function to be
subharmonic in a neighborhood of infinity is correct
then u(z) = |(z-1)/z^2| is a counterexample.

Any thoughts? Thanks.


************************

David C. Ullrich

.

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