Can anybody advise mathematical journals that publish research announcements? (I mean little papers without proofs.)
It sometimes happens that a proof is so long that it takes years to review and few journals are willing to accept it. I think in this case it would be useful (apart from posting your paper in arXiv) to announce the result in a short communication (this is how this problem is resolved in Russia, but I am asking about the rest of the world).
I am working in Functional analysis and in Geometry.
EDIT. More generally, I am curious,
how do people solve the problem of long texts?
Suppose you write a long text, where the main results are just several propositions, say, 5 theorems, and the rest are various technical lemmas, many of them, say, 100. Your text is devoted to the explanation of one idea, those 5 theorems appear only in the end, and it is impossible to separate them so that some of them could be proved in the middle of the text. As a corollary, it is impossible to divide your text into several papers, on 40-50 pages, so that they could be sent to usual journals.
You have to send this long paper to a journal, that publishes long texts, they will spend some time on finding a reviwer, he will check everything in your text, after that they will put your paper into the queue, and this is a long process, you understand... It can take 2-3-5 years before your paper will be published.
Of course, it will be difficult to explain to your employer, what you were doing the prevoius 5 years, when you were writing this paper.
So how do people resolve this problem? In Russia there is a possibility to write several little papers, without proofs, but with the formulations of the main results (those 5 theorems), then send them to some journals (together with that long text with accurate proofs), then the reviewer checks everything, agrees, they publish these little papers (this is much quicker, since these papers are little, there is no need to put them into a long queue), and everything is OK. As far as I understand, in France the situation is more or less similar. What about the rest of the world?