L'inégalité de Penrose
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.
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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