Results 1 to 10 of about 14,364,173 (167)

Curvature exponent and geodesic dimension on Sard-regular Carnot groups [PDF]

Analysis and Geometry in Metric Spaces, 2023
In this study, we characterize the geodesic dimension NGEO{N}_{{\rm{GEO}}} and give a new lower bound to the curvature exponent NCE{N}_{{\rm{CE}}} on Sard-regular Carnot groups.
Golo Sebastiano Nicolussi, Zhang Ye
doaj   +2 more sources

Convex Hull Property and Exclosure Theorems for H-Minimal Hypersurfaces in Carnot Groups [PDF]

Analysis and Geometry in Metric Spaces, 2016
In this paper, we generalize to sub-Riemannian Carnot groups some classical results in the theory of minimal submanifolds. Our main results are for step 2 Carnot groups.
Montefalcone Francescopaolo
doaj   +3 more sources

BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups

Analysis and Geometry in Metric Spaces, 2015
Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is a ball of G, then there exists a subset Z ⊂ B, whose image in H under f has small Hausdorff content, such that B\Z can be decomposed into a controlled number of pieces, the ...
Li Sean
doaj   +3 more sources

The Fractional Powers of the Sub-Laplacian in Carnot Groups Through an Analytic Continuation [PDF]

Journal of Geometric Analysis, 2023
In this paper we construct the fractional powers of the sub-Laplacian in Carnot groups through an analytic continuation approach. In addition, we characterize the powers of the fractional sub-Laplacian in the Heisenberg group, and as a byproduct we ...
Francesca Corni, Fausto Ferrari
semanticscholar   +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
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Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications [PDF]

Bollettino dell'Unione Matematica Italiana, 2023
In this paper, we provide a different approach to the Alt–Caffarelli–Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the gradient’s norm.
Fausto Ferrari, N. Forcillo
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
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Escape from compact sets of normal curves in Carnot groups [PDF]

E S A I M: Control, Optimisation and Calculus of Variations, 2023
In the setting of subFinsler Carnot groups, we consider curves that satisfy the normal equation coming from the Pontryagin Maximum Principle. We show that, unless it is constant, each such a curve leaves every compact set, quantitatively.
E. Donne, Nicola Paddeu
semanticscholar   +1 more source

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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On the H.-Q. Li inequality on step-two Carnot groups

Comptes Rendus. Mathématique, 2023
In this note we show that the gradient estimate of the heat semigroup, or more precisely the H.-Q. Li inequality, is preserved under tensorization, some suitable group epimorphism, and central sum. We also establish the Riemannian counterpart of the H.-Q.
Zhang, Ye
doaj   +1 more source