### Abstract

We consider the space of polynomial-growth harmonic forms. We prove that the dimension of such spaces must be finite and can be estimated if the metric is uniformly equivalent to one with asymptotically nonnegative curvature operator. This implies that the space of harmonic forms of polynomial growth order on the connected sum manifolds with nonnegative curvature operator must be finite-dimensional, which generalizes work of Tam.

Original language | English |
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Pages (from-to) | 91-109 |

Number of pages | 19 |

Journal | Pacific Journal of Mathematics |

Volume | 232 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 Sep 1 |

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### Keywords

- Curvature operator
- Harmonic forms

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Pacific Journal of Mathematics*,

*232*(1), 91-109. https://doi.org/10.2140/pjm.2007.232.91

**Dimension estimate of harmonic forms on complete manifolds.** / Ray Chen, Jui Tang; Anna Sung, Chiung Jue.

Research output: Contribution to journal › Article

*Pacific Journal of Mathematics*, vol. 232, no. 1, pp. 91-109. https://doi.org/10.2140/pjm.2007.232.91

}

TY - JOUR

T1 - Dimension estimate of harmonic forms on complete manifolds

AU - Ray Chen, Jui Tang

AU - Anna Sung, Chiung Jue

PY - 2007/9/1

Y1 - 2007/9/1

N2 - We consider the space of polynomial-growth harmonic forms. We prove that the dimension of such spaces must be finite and can be estimated if the metric is uniformly equivalent to one with asymptotically nonnegative curvature operator. This implies that the space of harmonic forms of polynomial growth order on the connected sum manifolds with nonnegative curvature operator must be finite-dimensional, which generalizes work of Tam.

AB - We consider the space of polynomial-growth harmonic forms. We prove that the dimension of such spaces must be finite and can be estimated if the metric is uniformly equivalent to one with asymptotically nonnegative curvature operator. This implies that the space of harmonic forms of polynomial growth order on the connected sum manifolds with nonnegative curvature operator must be finite-dimensional, which generalizes work of Tam.

KW - Curvature operator

KW - Harmonic forms

UR - http://www.scopus.com/inward/record.url?scp=70349775622&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349775622&partnerID=8YFLogxK

U2 - 10.2140/pjm.2007.232.91

DO - 10.2140/pjm.2007.232.91

M3 - Article

AN - SCOPUS:70349775622

VL - 232

SP - 91

EP - 109

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -