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

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).

preprint2000arXivOpen access
Paul M. N. Feehan
math.APmath-phmath.MPmath.DG
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Paul M. N. Feehan

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