Lipschitz k-connectivity, Euclidean isoperimetric inequalities, and coning inequalities all
measure the difficulty of filling a k-dimensional cycle in a space by a (k+ 1)-dimensional …

We bound the higher-order Dehn functions and other filling invariants of certain Carnot
groups using approximation techniques. These groups include the higher-dimensional …

Asymptotic invariants, complexity of groups and related problems | Bulletin of Mathematical
Sciences Skip to main content SpringerLink Log in Menu Find a journal Publish with us Search …

The Dehn function measures the area of minimal discs that fill closed curves in a space; it is
an important invariant in analysis, geometry, and geometric group theory. There are several …

Scalable spaces are simply connected compact manifolds or finite complexes whose real
cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational …

We study the Dehn function of connected Lie groups. We show that this function is always
exponential or polynomially bounded, according to the geometry of weights and of the 2 …

For every k⩾ 3 k\geqslant3, we exhibit a simply connected kk‐nilpotent Lie group N k N_k
whose Dehn function behaves like nk n^k, while the Dehn function of its associated Carnot …

Baumslag's group is a finitely presented metabelian group with a\mathbb Z ≀\mathbb Z
subgroup. There is an analogue with an additional torsion relation in which this subgroup …

We show that Legendrian integral currents in a contact manifold that locally minimize the
mass among Legendrian competitors have a regular set which is open and dense in their …

We bound the higher-order Dehn functions and other filling invariants of certain Carnot
groups using approximation techniques. These groups include the higher-dimensional …