We generalize the Sakai theorem that says that every complex algebraic manifold of general type is measure hyperbolic. We introduce the notion of k-measure hyperbolicity for every Eisenman k-measure and, following Sakai, we consider an analogue Kk of the Kodaira logarithmic dimension which construction uses logarithmic k-forms. We show that a complex algebraic manifold is k-measure hyperbolic if K̄k(X) = dim X.
|Original language||English (US)|
|Number of pages||19|
|Journal||Indiana University Mathematics Journal|
|State||Published - Jun 1 1999|
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