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Comments to 1995-03-005
Comments on article:
Giovanni Forni; The cohomological equation for area-preserving flows on compact surfaces ERA Amer. Math. Soc. 01 (1995), pp. 114-123.
Added May 8, 1996 15:12:13 EDT
Comments by the author
A paper containing complete
proofs of all announced results entitled "Solutions of the
cohomological equation for area-preserving flows on higher genus
surfaces" will appear in Annals of Mathematics.
Added July 15, 1997 13:30:00 EDT
Comments by the author
Errata
The statement of Theorem A is not correct and has to be changed as
follows. The equation $Xu=f$ does not always have a solution
$u\in L^2_{loc}(M\setminus\Sigma)$ under the hypotheses of Theorem A.
However, under such hypotheses, there is always a distributional solution
$u\in {\Cal D}'(M\setminus\Sigma)$. Theorem A should be replaced by the
corresponding weaker statement. Theorems B and C stay unchanged. As a
consequence of the correction to Theorem A, we are not able any more to
give an independent proof of the generic ergodicity for the class of
flows
under consideration (Keane conjecture). The proof of Theorem B will
therefore
depend on Theorem A and on known proofs of the Keane conjecture, in
particular
by H.Masur and S.Kerckhoff-H.Masur-J.Smillie (see the bibliography of the
paper).
Updates to Bibliography
A paper containing complete proofs of the corrected version of the above
results
will appear in the September 1997 Issue of Annals of Mathematics.