Asymptotic behavior of the Riemannian Heisenberg group and its horoboundary View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-08

AUTHORS

Enrico Le Donne, Sebastiano Nicolussi-Golo, Andrea Sambusetti

ABSTRACT

The paper is devoted to the large-scale geometry of the Heisenberg group H equipped with left-invariant Riemannian metrics. We prove that two such metrics have bounded difference if and only if they are asymptotic, i.e., their ratio goes to one at infinity. Moreover, we show that for every left-invariant Riemannian metric d on H there is a unique subRiemannian metric d′ for which d-d′ goes to zero at infinity, and we estimate the rate of convergence. As a first immediate consequence, we get that the Riemannian Heisenberg group is at bounded distance from its asymptotic cone. The second consequence, which was our aim, is the explicit description of the horoboundary of the Riemannian Heisenberg group. More... »

PAGES

1251-1272

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10231-016-0615-2

DOI

http://dx.doi.org/10.1007/s10231-016-0615-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1036763296


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