Refined Kato inequalities and conformal weights in Riemannian geometry

1999/09/21 by David M. J. Calderbank, Paul Gauduchon, Marc Herzlich · 3 citations
Mathematics · #math.DG #math.AP #math.FA #msc:53B21 #msc:58G03

paper · pdf

published as J. Funct. Anal. 173 (2000) 214-255 · AMS-LaTeX, 36pp, 1 figure (region.eps)

arxiv created 1999/09/21 · arxiv updated 2009/11/30

Abstract

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.

Cited by

• The positive mass theorem under a spectral scalar curvature bound on spin manifolds
• Geometric Rigidity via Almost-Harmonic Twisted Spinors
• Decomposition of the Curvature Operator and Applications to the Hopf Conjecture

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