Comments to 1995-03-005

Outdated Archival Version

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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.