Harmonic discs of solutions to the complex homogeneous Monge-Ampère equationPublications Mathématiques de l'Institut des Hautes Études Scientifiques - Tập 122 - Trang 315-335 - 2015
Julius Ross, David Witt Nyström
We study regularity properties of solutions to the Dirichlet problem for the complex Homogeneous Monge-Ampère equation. We show that for certain boundary data on P
1 the solution Φ to this Dirichlet problem is connected via a Legendre transform to an associated flow in the complex plane called the Hele-Shaw flow. Using this we determine precisely the harmonic discs associat...... hiện toàn bộ
The space of metrics of positive scalar curvaturePublications Mathématiques de l'Institut des Hautes Études Scientifiques - - 2014
Bernhard Hanke, Thomas Schick, Wolfgang Steimle
We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements in higher homotopy and homology groups of these spaces, which, in contrast to previous approaches, are of infinite order and survive in the (observer) moduli space of such metrics. Along the way we construct smooth fiber bundles over sphere...... hiện toàn bộ
The word and Riemannian metrics on lattices of semisimple groupsPublications Mathématiques de l'Institut des Hautes Études Scientifiques - Tập 91 - Trang 5-53 - 2000
Alexander Lubotzky, Shahar Mozes, M. S. Raghunathan
Let G be a semisimple Lie group of rank ⩾2 and Γ an irreducible lattice. Γ has two natural metrics: a metric inherited from a Riemannian metric on the ambient Lie group and a word metric defined with respect to some finite set of generators. Confirming a conjecture of D. Kazhdan (cf. Gromov [Gr2]) we show that these metrics are Lipschitz equivalent. It is shown that a cyclic subgroup of Γ is virtu...... hiện toàn bộ
The stable theoryPublications Mathématiques de l'Institut des Hautes Études Scientifiques - Tập 15 - Trang 75-89 - 1963
Constructing group actions on quasi-trees and applications to mapping class groupsPublications Mathématiques de l'Institut des Hautes Études Scientifiques - Tập 122 - Trang 1-64 - 2014
Mladen Bestvina, Ken Bromberg, Koji Fujiwara
A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary (relatively) hyperbolic groups, CAT(0) groups with rank 1 elements, mapping class groups and Out(F
n
). As an application, we show that mapping class gro...... hiện toàn bộ