Results 11 to 20 of about 1,124 (81)
A Cornucopia of Carnot Groups in Low Dimensions
Analysis and Geometry in Metric Spaces, 2022 Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating.
Le Donne Enrico, Tripaldi Francesca
doaj +1 more source
A partial solution of the isoperimetric problem for the Heisenberg group [PDF]
, 2006 We provide a solution to the isoperimetric problem in the Heisenberg group ℍ n when the competing sets belong to a restricted class of C 2 graphs. Within this restricted class we characterize the isoperimetric profiles as the bubble sets (1.5) (modulo ...
D. Danielli, N. Garofalo, D. Nhieu
semanticscholar +1 more source
On sets with unit Hausdorff density in homogeneous groups
Forum of Mathematics, Sigma, 2023 It is a longstanding conjecture that given a subset E of a metric space, if E has unit $\mathscr {H}^{\alpha }\llcorner E$ -density almost everywhere, then E is an $\alpha $ -rectifiable set. We prove this conjecture under the assumption that
Antoine Julia, Andrea Merlo
doaj +1 more source
Identifying 1-rectifiable measures in Carnot groups
Analysis and Geometry in Metric Spaces, 2023 We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, extending a theorem of M. Badger and R.
Badger Matthew, Li Sean, Zimmerman Scott
doaj +1 more source
On some geometric properties of currents and Frobenius theorem [PDF]
, 2017 In this note we announce some results, due to appear in [2], [3], on the structure of integral and normal currents, and their relation to Frobenius theorem.
Alberti, Giovanni, Massaccesi, Annalisa
core +2 more sources
Non-minimality of corners in subriemannian geometry [PDF]
, 2016 We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities.
C Golé +13 more
core +2 more sources
Analysis and Geometry in Metric Spaces, 2018 Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance.
Le Donne Enrico
doaj +1 more source
A survey on Inverse mean curvature flow in ROSSes
Complex Manifolds, 2017 In this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces.
Pipoli Giuseppe
doaj +1 more source
Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces
Analysis and Geometry in Metric Spaces, 2013 We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of
Balogh Zoltán M. +2 more
doaj +1 more source
Topology and Integrability in Lagrangian Mechanics
, 2017 This chapter reviews complete integrability in the setting of Lagrangian/Hamiltonian mechanics. It includes the construction of angle-action variables in illustrative examples, along with a proof of the Liouville-Arnol’d theorem.
L. Butler
semanticscholar +1 more source