Dimension estimate of polynomial growth harmonic forms

Jui-Tang Chen, Chiung Jue Anna Sung

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let Hpl (M) be the space of polynomial growth harmonic forms. We proved that the dimension of such spaces must be finite and can be estimated if the metric is uniformly equivalent to one with a nonnegative curvature operator. In particular, this implies that the space of harmonic forms of fixed growth order on the Euclidean space with any periodic metric must be finite dimensional.

Original languageEnglish
Pages (from-to)167-183
Number of pages17
JournalJournal of Differential Geometry
Volume73
Issue number1
DOIs
Publication statusPublished - 2006 Jan 1

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Harmonic Forms
Polynomial Growth
Estimate
Metric
Nonnegative Curvature
Euclidean space
Imply
Operator

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Dimension estimate of polynomial growth harmonic forms. / Chen, Jui-Tang; Anna Sung, Chiung Jue.

In: Journal of Differential Geometry, Vol. 73, No. 1, 01.01.2006, p. 167-183.

Research output: Contribution to journalArticle

Chen, Jui-Tang ; Anna Sung, Chiung Jue. / Dimension estimate of polynomial growth harmonic forms. In: Journal of Differential Geometry. 2006 ; Vol. 73, No. 1. pp. 167-183.
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