Results 1 to 10 of about 89 (67)
Unextendable Intrinsic Lipschitz Curves: [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2021 In the setting of Carnot groups, we exhibit examples of intrinisc Lipschitz curves of positive H1measure that intersect every connected intrinsic Lipschitz curve in a H1-negligible set.
G. Antonelli, Andrea Merlo
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On rectifiable measures in Carnot groups: Marstrand–Mattila rectifiability criterion [PDF]
Journal of Functional Analysis, 2022 In this paper we continue the study of the notion of P-rectifiability in Carnot groups. We say that a Radon measure is Ph-rectifiable, for h ∈ N, if it has positive h-lower density and finite h-upper density almost everywhere, and, at almost every point,
G. Antonelli, Andrea Merlo
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Exceptional families of measures on Carnot groups
Analysis and Geometry in Metric Spaces, 2023 We study the families of measures on Carnot groups that have vanishing pp-module, which we call Mp{M}_{p}-exceptional families. We found necessary and sufficient Conditions for the family of intrinsic Lipschitz surfaces passing through a common point to ...
Franchi Bruno, Markina Irina
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On the heat diffusion for generic Riemannian and sub-Riemannian structures [PDF]
, 2013 In this paper we provide the small-time heat kernel asymptotics at the cut locus in three relevant cases: generic low-dimensional Riemannian manifolds, generic 3D contact sub-Riemannian manifolds (close to the starting point) and generic 4D quasi-contact
D. Barilari +3 more
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A proof of a trace formula by Richard Melrose
Advanced Nonlinear Studies, 2023 The goal of this article is to give a new proof of the wave trace formula proved by Richard Melrose in an impressive article. This trace formula is an extension of the Chazarain-Duistermaat-Guillemin trace formula (denoted as “CDG trace formula” in this ...
Colin de Verdière Yves
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Geodesics and horizontal-path spaces in Carnot groups [PDF]
, 2013 We study properties of the space of horizontal paths joining the origin with a vertical point on a generic two-step Carnot group. The energy is a Morse-Bott functional on paths and its critical points (sub-Riemannian geodesics) appear in families ...
A. Agrachev +2 more
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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
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Stable solutions of symmetric systems involving hypoelliptic operators [PDF]
Journal of Functional Analysis, 2017 Let X and Y be two noncommuting vector fields in an open set Ω in a manifold M equipped with a sub-Riemannian structure. We examine stable solutions of the following symmetric system ∆XY ui = Hi(u1, · · · , um) in Ω for 1 ≤ i ≤ m, when the operator ∆XY ...
Mostafa Fazly
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Sub-Finsler Horofunction Boundaries of the Heisenberg Group
Analysis and Geometry in Metric Spaces, 2021 We give a complete analytic and geometric description of the horofunction boundary for polygonal sub-Finsler metrics, that is, those that arise as asymptotic cones of word metrics, on the Heisenberg group.
Fisher Nate, Golo Sebastiano Nicolussi
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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
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