A Kato-Yau inequality and decay estimate for eigenspinors

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We show that harmonic spinors obey a strengthened version of the well-known pointwise Kato inequality for sections of a vector bundle with a connection. We then give two different proofs an interesting decay estimate for harmonic spinors, one using our Kato-Yau estimate and resulting differential inequality, and a second using known eigenvalue calculations for the Dirac operator on the three-sphere. As an example of the use of these estimates, we also describe some new applications to the problems of gluing and ungluing PU(2) monopoles.

Original languageEnglish (US)
Pages (from-to)469-489
Number of pages21
JournalJournal of Geometric Analysis
Issue number3
StatePublished - 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


  • Dirac operator
  • Kato-Yao inequality
  • decay estimate
  • harmonic spinor


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