Dimension estimate of harmonic forms on complete manifolds

Jui Tang Ray Chen, Chiung Jue Anna Sung

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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

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Keywords

  • Curvature operator
  • Harmonic forms

ASJC Scopus subject areas

  • Mathematics(all)

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