There is a ticket for GAE Vaadin support: http://dev.vaadin.com/ticket/2835
I tried - and id works. First of all you need to enable sessions:
<sessions-enabled>true</sessions-enabled>
and use the GAEApplicationServlet instead of the standard vaadin's.
Secondly: make sure that all objects in the domain are serializable (I'm sure this is not a problem, by the way)
And thirdly: move all static files (css theme and images) from vaadin jar to your webapp folder
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