1,720,958 research outputs found
Connected surfaces with boundary minimizing the Willmore energy
Full text linkFor a given family of smooth closed curves gamma(1),...,gamma(alpha) subset of R-3 we consider the problem of finding an elastic connected compact surface M with boundary gamma = gamma(1) boolean OR ... boolean OR gamma(alpha). This is realized by minimizing the Willmore energy W on a suitable class of competitors. While the direct minimization of the Area functional may lead to limits that are disconnected, we prove that, if the infimum of the problem is < 4 pi, there exists a connected compact minimizer of W in the class of integer rectifiable curvature varifolds with the assigned boundary conditions. This is done by proving that varifold convergence of bounded varifolds with boundary with uniformly bounded Willmore energy implies the convergence of their supports in Hausdorff distance. Hence, in the cases in which a small perturbation of the boundary conditions causes the non-existence of Area-minimizing connected surfaces, our minimization process models the existence of optimal elastic connected compact generalized surfaces with such boundary data. We also study the asymptotic regime in which the diameter of the optimal connected surfaces is arbitrarily large. Under suitable boundedness assumptions, we show that rescalings of such surfaces converge to round spheres. The study of both the perturbative and the asymptotic regime is motivated by the remarkable case of elastic surfaces connecting two parallel circles located at any possible distance one from the other. The main tool we use is the monotonicity formula for curvature varifolds ([15, 31]) that we extend to varifolds with boundary, together with its consequences on the structure of varifolds with bounded Willmore energy
The isoperimetric problem on Riemannian manifolds via Gromov-Hausdorff asymptotic analysis
No full textIn this paper, we prove the existence of isoperimetric regions of any volume in Riemannian manifolds with Ricci bounded below assuming Gromov-Hausdorff asymptoticity to the suitable simply connected model of constant sectional curvature. The previous result is a consequence of a general structure theorem for perimeter-minimizing sequences of sets of fixed volume on noncollapsed Riemannian manifolds with a lower bound on the Ricci curvature. We show that, without assuming any further hypotheses on the asymptotic geometry, all the mass and the perimeter lost at infinity, if any, are recovered by at most countably many isoperimetric regions sitting in some (possibly nonsmooth) Gromov-Hausdorff limits at infinity. The Gromov-Hausdorff asymptotic analysis allows us to recover and extend different previous existence theorems. While studying the isoperimetric problem in the smooth setting, the nonsmooth geometry naturally emerges, and thus our treatment combines techniques from both the theories
Degenerate Elastic Networks
Full text linkWe minimize a linear combination of the length and the L2-norm of the curvature among networks in Rd belonging to a given class determined by the number of curves, the order of the junctions, and the angles between curves at the junctions. Since this class lacks compactness, we characterize the set of limits of sequences of networks bounded in energy, providing an explicit representation of the relaxed problem. This is expressed in terms of the new notion of degenerate elastic networks that, rather surprisingly, involves only the properties of the given class, without reference to the curvature. In the case of d= 2 we also give an equivalent description of degenerate elastic networks by means of a combinatorial definition easy to validate by a finite algorithm. Moreover we provide examples, counterexamples, and additional results that motivate our study and show the sharpness of our characterization
On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
Full text linkIn this paper we provide new existence results for isoperimetric sets of large volume in Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth. We find sufficient conditions for their existence in terms of the geometry at infinity of the manifold. As a byproduct we show that isoperimetric sets of big volume always exist on manifolds with nonnegative sectional curvature and Euclidean volume growth. Our method combines an asymptotic mass decomposition result for minimizing sequences, a sharp isoperimetric inequality on nonsmooth spaces, and the concavity property of the isoperimetric profile. The latter is new in the generality of noncollapsed manifolds with Ricci curvature bounded below
Minimizing properties of networks via global and local calibrations
Full text linkIn this note we prove that minimal networks enjoy minimizing properties for
the length functional. A minimal network is, roughly speaking, a subset of
composed of straight segments joining at triple junctions
forming angles equal to ; in particular such objects are just
critical points of the length functional a priori.
We show that a minimal network : i) minimizes mass among currents
with coefficients in a suitable group having the same boundary of ,
ii) identifies the interfaces of a partition of a neighborhood of
solving the minimal partition problem among partitions with same boundary
traces.
Consequences and sharpness of such results are discussed. The proofs reduce
to rather simple and direct arguments based on the exhibition of (global or
local) calibrations associated to the minimal network
{\L}ojasiewicz-Simon inequalities for minimal networks: stability and convergence
Full text linkWe investigate stability properties of the motion by curvature of planar
networks. We prove Lojasiewicz-Simon gradient inequalities for the length
functional of planar networks with triple junctions. In particular, such an
inequality holds for networks with junctions forming angles equal to
that are close in -norm to minimal networks, i.e., networks
whose edges also have vanishing curvature. The latter inequality bounds a
concave power of the difference between length of a minimal network
and length of a triple junctions network from above by the -norm
of the curvature of the edges of . We apply this result to prove the
stability of minimal networks in the sense that a motion by curvature starting
from a network sufficiently close in -norm to a minimal one exists for all
times and smoothly converges. We further rigorously construct an example of a
motion by curvature having uniformly bounded curvature that smoothly converges
to a degenerate network in infinite time
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
- …
