A Kato-Yau inequality for harmonic spinors and decay estimate for eigenspinors

Details A Kato-Yau inequality for harmonic spinors and decay estimate for eigenspinors A Kato-Yau inequality for harmonic spinors and decay estimate for eigenspinors

1999-03-02

arxiv.org/abs/math/9903021v4

J. Geom. Anal. 11 (2001), 469 - 489.

Mathematics

Differential Geometry

19 pages, Latex 2e. The article has been revised for publication. Journal of Geometric Analysis, to appear

Scientific paper

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 prove a decay estimate for eigenspinors using this Kato-Yau estimate and resulting differential inequality. We briefly describe some applications to gauge theory---specifically to integral estimates which are used when gluing and ungluing PU(2) monopoles (math.DG/9907107).

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