The conjugacy problem for relatively hyperbolic groups.
The diameter function on the space of space form
The Existence of Polarized F-structure on Volume Collapsed 4-manifolds.
The filling radius of homogeneous manifolds
The isometry groups of Riemannian orbifolds.
The Morse landscape of a riemannian disk
We study upper bounds on the length functional along contractions of loops in Riemannian disks of bounded diameter and circumference. By constructing metrics adapted to imbedded trees of increasing complexity, we reduce the nonexistence of such upper bounds to the study of a topological invariant of imbedded finite trees. This invariant is related to the complexity of the binary representation of integers. It is also related to lower bounds on the number of points in level sets of a real-valued...
The proportionality constant for the simplicial volume of locally symmetric spaces
We follow ideas going back to Gromov's seminal article [Publ. Math. IHES 56 (1982)] to show that the proportionality constant relating the simplicial volume and the volume of a closed, oriented, locally symmetric space M = Γ∖G/K of noncompact type is equal to the Gromov norm of the volume form in the continuous cohomology of G. The proportionality constant thus becomes easier to compute. Furthermore, this method also gives a simple proof of the proportionality principle for arbitrary manifolds.
The Trapping Property of Totally Geodesic Hyperplanes in Hadamard Spaces.
Théorème de la sphère
Trees of manifolds and boundaries of systolic groups
We prove that the Pontryagin sphere and the Pontryagin nonorientable surface occur as the Gromov boundary of a 7-systolic group acting geometrically on a 7-systolic normal pseudomanifold of dimension 3.