Results 11 to 20 of about 61 (61)

On Conditions for Unrectifiability of a Metric Space

Analysis and Geometry in Metric Spaces, 2014
We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(f(E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a ...
Hajłasz Piotr, Malekzadeh Soheil
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Existence of isoperimetric regions in sub-Finsler nilpotent groups

Analysis and Geometry in Metric Spaces
We consider a nilpotent Lie group with a bracket-generating distribution ℋ{\mathcal{ {\mathcal H} }} and an asymmetric left-invariant norm ∣⋅∣K{| \cdot | }_{K} induced by a convex body K⊆RkK\subseteq {{\mathbb{R}}}^{k} containing 0 in its interior.
Pozuelo Julián
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Metric lines in the jet space

Analysis and Geometry in Metric Spaces
In the realm of sub-Riemannian manifolds, a relevant question is: what are the metric lines (isometric embedding of the real line)? The space of kk-jets of a real function of one real variable xx, denoted by Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}),
Bravo-Doddoli Alejandro
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Uniform spaces, coarse spaces, dilation spaces

, 2020
WARNING: WORKING VERSION, NOT FINAL, THANKS FOR COMMENTS.
Marius Buliga
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On an evolution equation in sub-Finsler geometry

Analysis and Geometry in Metric Spaces
We study the gradient flow of an energy with mixed homogeneity, which is at the interface of Finsler and sub-Riemannian geometry.
Garofalo Nicola
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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
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On the role of embeddability in conformal pseudo-hermitian geometry

Analysis and Geometry in Metric Spaces
In this article, we review some recent results about the role of embeddability in conformal CR (Cauchy-Riemann) geometry. We will show how this condition enters in the second variation of the pseudo-hermitian counterpart of the Einstein-Hilbert action ...
Malchiodi Andrea
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Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates

Advanced Nonlinear Studies
On general Carnot groups, the definition of a possible hypoelliptic Hodge-Laplacian on forms using the Rumin complex has been considered in (M. Rumin, “Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie ...
Baldi Annalisa, Tripaldi Francesca
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Capacity and perimeter from logarithmic fractional Sobolev spaces on Carnot groups

Advances in Nonlinear Analysis
In this paper, we introduce the logarithmic fractional Sobolev space on Carnot groups and investigate the various functional-geometric aspects of the corresponding functional capacity.
Zhao Nan, Liu Yu
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Analytic torsion of nilmanifolds with (2, 3, 5) distributions

Analysis and Geometry in Metric Spaces
We consider generic rank two distributions on five-dimensional nilmanifolds and show that the analytic torsion of their Rumin complex coincides with the Ray-Singer torsion.
Haller Stefan
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