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

Abstract

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).

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

References in corpus (1)

• PU(2) monopoles and relations between four-manifold invariants

Cited by in corpus (1)

• ${\mathrm{G}}_2$-instantons on generalised Kummer constructions