Dimension estimate of harmonic forms on complete manifolds

Jui Tang Ray Chen, Chiung Jue Anna Sung

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)91-109
Number of pages19
JournalPacific Journal of Mathematics
Volume232
Issue number1
DOIs
Publication statusPublished - 2007 Sep 1

Fingerprint

Harmonic Forms
Nonnegative Curvature
Polynomial Growth
Estimate
Connected Sum
Operator
Imply
Metric
Generalise

Keywords

  • Curvature operator
  • Harmonic forms

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Pacific Journal of Mathematics, Vol. 232, No. 1, 01.09.2007, p. 91-109.

Research output: Contribution to journalArticle

Ray Chen, Jui Tang ; Anna Sung, Chiung Jue. / Dimension estimate of harmonic forms on complete manifolds. In: Pacific Journal of Mathematics. 2007 ; Vol. 232, No. 1. pp. 91-109.
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