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Refined Kato inequalities in riemannian geometry

Marc Herzlich — 2000

Journées équations aux dérivées partielles

We describe the recent joint work of the author with David M. J. Calderbank and Paul Gauduchon on refined Kato inequalities for sections of vector bundles living in the kernel of natural first-order elliptic operators.

Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces

Hassan BoualemMarc Herzlich — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Any Kähler metric on the ball which is strongly asymptotic to complex hyperbolic space and whose scalar curvature is no less than the one of the complex hyperbolic space must be isometrically biholomorphic to it. This result has been known for some time in odd complex dimension and we provide here a proof in even dimension.

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