Results 1 to 10 of about 1,106 (82)
The Lichnerowicz theorem on CR manifolds [PDF]
arXiv, 2006 We obtain a Bochner type formula and an estimate from below on the spectrum of the sublaplacian of a compact strictly pseudoconvex CR manifold.
Barletta, Elisabetta
arxiv +6 more sources
Rigidity of fiber-preserving quasisymmetric maps [PDF]
arXiv, 2015 We show that fiber-preserving quasisymmetric maps are biLipschitz. As an application, we show that quasisymmetric maps on Carnot groups with reducible first stratum are biLipschitz.
Donne, Enrico Le, Xie, Xiangdong
arxiv +3 more sources
On an evolution equation in sub-Finsler geometry [PDF]
Analysis and Geometry in Metric SpacesWe study the gradient flow of an energy with mixed homogeneity, which is at the interface of Finsler and sub-Riemannian geometry.
Garofalo Nicola
doaj +2 more sources
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.
Gioacchino Antonelli, Andrea Merlo
semanticscholar +1 more source
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
doaj +1 more source
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
doaj +1 more source
The geometry of Riemannian curvature radii [PDF]
Journal of dynamical and Control Systems 29, (2023), 1829-1853, 2022 In this paper we explore the geometric structures associated with curvature radii of curves with values on a Riemannian manifold $(M, g)$. We show the existence of sub-Riemannian manifolds naturally associated with the curvature radii and we investigate their properties. The main character of our construction is a pair of global vector fields $f_1, f_2$
arxiv +1 more source
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
semanticscholar +1 more source
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
doaj +1 more source
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
semanticscholar +1 more source