Results 11 to 20 of about 14,687 (238)

Sharp measure contraction property for generalized H-type Carnot groups [PDF]

, 2017
We prove that H-type Carnot groups of rank $k$ and dimension $n$ satisfy the $\mathrm{MCP}(K,N)$ if and only if $K\leq 0$ and $N \geq k+3(n-k)$. The latter integer coincides with the geodesic dimension of the Carnot group.
Davide Barilari, Luca Rizzi
openalex   +6 more sources

Geometric inequalities in Carnot groups [PDF]

Pacific Journal of Mathematics, 2012
Let $\GG$ be a sub-Riemannian $k$-step Carnot group of homogeneous dimension $Q$. In this paper, we shall prove several geometric inequalities concerning smooth hypersurfaces (i.e.
Montefalcone, Francescopaolo
core   +3 more sources

Yamabe-type equations on Carnot groups

Potential Analysis, 2016
This article is concerned with a class of elliptic equations on Carnot groups depending of one real positive parameter and involving a critical nonlinearity.
Bisci, Giovanni Molica, Repovš, Dušan D.   +1 more
core   +6 more sources

BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups [PDF]

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   +2 more sources

Isodiametric inequality in Carnot groups

Annales Academiae Scientiarum Fennicae Mathematica, 2010
The classical isodiametric inequality in the Euclidean space says that balls maximize the volume among all sets with a given diameter. We consider in this paper the case of Carnot groups.
Rigot, Severine
core   +7 more sources

Rearrangements in Carnot Groups [PDF]

Acta Mathematica Sinica, English Series, 2019
In this paper we extend the notion of rearrangement of nonnegative functions to the setting of Carnot groups. We define rearrangement with respect to a given family of anisotropic balls B_r or equivalently with respect to a gauge |x|, and prove basic regularity properties of this construction.
Manfredi, Juan J., Vera de Serio, Virginia N.   +1 more
openaire   +2 more sources

Harnessing Colloidal Dispersion for Laccase-Driven Enzymatic Depolymerization of Polystyrene. [PDF]

Angew Chem Int Ed Engl
Polystyrene (PS), long considered non‐degradable by biocatalytic pathways, can now be broken down under aqueous conditions using atmospheric air and a laccase–mediator system composed of a commercially available fungal enzyme and 1‐hydroxybenzotriazole as small organic mediator.
Pujol M, Gonsales SA, Seksek F, Berrin JG, Bissaro B, Taton D.   +5 more
europepmc   +3 more sources

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

Notions of Convexity in Carnot Groups [PDF]

Communications in Analysis and Geometry, 2003
The aim of this interesting paper is to study appropriate notions of convexity in the setting of Carnot groups \(G\). First, the notion of strong \(H\)-convexity is examined. Some arguments showing that the concept is to restrictive are presented. Then the notion of weakly \(H\)-convex functions is defined.
DANIELLI D., GAROFALO, NICOLA, NHIEU D. M.   +2 more
openaire   +4 more sources

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