1,720,976 research outputs found
Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates
Full text linkOn 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 groups,” C. R. Acad. Sci., Paris Sér. I Math., vol. 329, no. 11, pp.
985–990, 1999, M. Rumin, “Sub-Riemannian limit of the differential form spectrum of contactmanifolds,” Geom.
Funct. Anal., vol. 10, no. 2, pp. 407–452, 2000), where the author introduced a 0-order pseudodifferential operator
on forms. However, for questions regarding regularity for example, where one needs sharp estimates, this
0-order operator is not suitable. Up to now, there have only been very few attempts to define hypoelliptic Hodge-
Laplacians on forms that would allow for such sharp estimates. Indeed, this question is rather difficult to address
in full generality, the main issue being that the Rumin exterior differential dc is not homogeneous on arbitrary
Carnot groups. In this note, we consider the specific example of the free Carnot group of step 3 with 2 generators,
and we introduce three possible definitions of hypoelliptic Hodge-Laplacians.We compare how these three possible
Laplacians can be used to obtain sharp div-curl type inequalities akin to those considered by Bourgain &
Brezis and Lanzani & Stein for the de Rham complex, or their subelliptic counterparts obtained by Baldi, Franchi
& Pansu for the Rumin complex on Heisenberg groups
On the topology of surfaces with the generalised simple lift property
Full text linkIn this paper, we study the geometry of surfaces with the generalised simple lift property. This work generalises previous results by Bernstein and Tinaglia (J Differ Geom 102(1):1–23, 2016) and it is motivated by the fact that leaves of a minimal lamination obtained as a limit of a sequence of property embedded minimal disks satisfy the generalised simple lift property.peerReviewe
Extending an example by Colding and Minicozzi
Full text linkExtending an example by Colding and Minicozzi (Trans Am Math Soc 356(1):283–289, 2003), we construct a sequence of properly embedded minimal disks \Sigma _i in an infinite Euclidean cylinder around the x_3-axis with curvature blow-up at a single point. The sequence converges to a non-smooth and non-proper minimal lamination in the cylinder. Moreover, we show that the disks \Sigma _i are not properly embedded in a sequence of open subsets of \mathbb {R}^3 that exhausts \mathbb {R}^3.peerReviewe
Gagliardo-Nirenberg Inequalities for Horizontal Vector Fields in the Engel Group and in the Seven-Dimensional Quaternionic Heisenberg Group
No full textRecently, Bourgain & Brezis and Lanzani & Stein considered a class of div-curl inequalities in de Rham's complex.
In this note we prove the natural counterpart of these inequalities for
horizontal vector fields in the Engel group and in the 7-dimensional quaternionic Heisenberg group
A Cornucopia of Carnot Groups in Low Dimensions
Full text linkStratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating. When a stratified group is equipped with a left-invariant path distance that is homogeneous with respect to the automorphisms induced by the derivation,this metric space is known as Carnot group. Carnot groups appear in several mathematical contexts. To understand their algebraic structure, it is useful to study some examples explicitly. In this work, we provide a list of low-dimensional stratified groups, express their Lie product, and present a basis of left-invariant vector fields, together with their respective left-invariant 1-forms, a basis of right-invariant vector fields, and some other properties. We exhibit all stratified groups in dimension up to 7 and also study some free-nilpotent groups in dimension up to 14
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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