Refined Kato inequalities and conformal weights in Riemannian geometry

Details Refined Kato inequalities and conformal weights in Riemannian geometry Refined Kato inequalities and conformal weights in Riemannian geometry

1999-09-21

arxiv.org/abs/math/9909116v1

J. Funct. Anal. 173 (2000) 214-255

Mathematics

Differential Geometry

AMS-LaTeX, 36pp, 1 figure (region.eps)

Scientific paper

We establish refinements of the classical Kato inequality for sections of a vector bundle which lie in the kernel of a natural injectively elliptic first-order linear differential operator. Our main result is a general expression which gives the value of the constants appearing in the refined inequalities. These constants are shown to be optimal and are computed explicitly in most practical cases.

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