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Compatible complex structures on twistor space

Guillaume Deschamps (2011)

Annales de l’institut Fourier

Let M be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space Z admits a natural metric. The aim of this article is to study properties of complex structures on Z which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on M (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space Z .

Empilements de cercles et modules combinatoires

Peter HaÏssinsky (2009)

Annales de l’institut Fourier

Le but de cette note est de tenter d’expliquer les liens étroits qui unissent la théorie des empilements de cercles et des modules combinatoires et de comparer les approches à la conjecture de J.W. Cannon qui en découlent.

Layered circle packings.

Dennis, David, Williams, G. Brock (2005)

International Journal of Mathematics and Mathematical Sciences

Perturbing the hexagonal circle packing: a percolation perspective

Itai Benjamini, Alexandre Stauffer (2013)

Annales de l'I.H.P. Probabilités et statistiques

We consider the hexagonal circle packing with radius 1 / 2 and perturb it by letting the circles move as independent Brownian motions for time t . It is shown that, for large enough t , if 𝛱 t is the point process given by the center of the circles at time t , then, as t , the critical radius for circles centered at 𝛱 t to contain an infinite component converges to that of continuum percolation (which was shown – based on a Monte Carlo estimate – by Balister, Bollobás and Walters to be strictly bigger than...

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