### Abstract

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 K_{k} of the Kodaira logarithmic dimension which construction uses logarithmic k-forms. We show that a complex algebraic manifold is k-measure hyperbolic if K̄_{k}(X) = dim X.

Original language | English (US) |
---|---|

Pages (from-to) | 449-467 |

Number of pages | 19 |

Journal | Indiana University Mathematics Journal |

Volume | 48 |

Issue number | 2 |

State | Published - Jun 1999 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Indiana University Mathematics Journal*,

*48*(2), 449-467.

**Eisenman intrinsic measures and algebraic invariants.** / Kaliman, Shulim.

Research output: Contribution to journal › Article

*Indiana University Mathematics Journal*, vol. 48, no. 2, pp. 449-467.

}

TY - JOUR

T1 - Eisenman intrinsic measures and algebraic invariants

AU - Kaliman, Shulim

PY - 1999/6

Y1 - 1999/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0038936620&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038936620&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0038936620

VL - 48

SP - 449

EP - 467

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 2

ER -