1,720,998 research outputs found
The State of the Art of Bernstein's Problem
No full textWether the only minimal stable complete hypersurfaces in R^{n+1}, with 2< n < 8 are hyperplanes, is an open problem. We describe its historical motivations and our results obtained by exploring it
Stably Embedded Minimal Hypersurfaces
No full textWe use Schoen-Simon-Yau's curvature estimates to prove that the subfocal
tubular neighborhood of a non planar minimal hypersurface with bounded
second fundamental form, stably embedded in R^{n+1}, n < 5, whose radius
decays sufficiently slowly can not be embedded. In particular such hypersurfaces
admit no embedded tubular neighborhoods of constant radius, whatever
small the radius. However, assuming a further hypothesis on the embedding,
we prove that such hypersurfaces admit an embedded tube whose
radius decays sufficiently fast
Caccioppoli’s inequalities on constant mean curvature hypersurfaces in Riemannian Manifolds
No full textWe prove some Caccioppoli's inequalities for the traceless part of the second fundamental
form of a complete, non compact, nite index, constant mean curvature hypersurface of a
Riemannian manifold, satisfying some curvature conditions. This allows us to unify and clarify
many results in the literature and to obtain some new results. For example, we prove that
there is no stable, complete, non compact hypersurface in Rn+1; n 5; with constant mean
curvature H 6= 0; provided that, for suitable p; the Lp-norm of the traceless part of second
fundamental form satises some growth conditio
Mixed gravitational field equations on globally hyperbolic spacetimes
Full text linkFor every globally hyperbolic spacetime we derive new mixed gravitational field equations embodying the smooth Geroch infinitesimal splitting of , as exhibited by A.N. Bernal & M. Sanchez. We give sufficient geometric conditions for the existence of exact solutions to mixed field equations in free space. We linearize and solve the mixed field equations for empty space, where is the mixed scalar curvature of foliated spacetime . If is a solution to the linearized
field equations then each leaf of is totally geodesic in to order . We derive the equations of motion of a material particle in gravitational field governed by the mixed field equations
. In the weak field () and low velocity () limit the motion equations are
d^2 \mathb{ r}/dt^2 = \nabla \phi + \mathbf{F} where
A Note on Constant Mean Curvature Foliations of Noncompact Riemannian Manifolds
Full text linkWe aimed to study constant mean curvature foliations of noncompact Riemannian manifolds, satisfying some geometric constraints. As a byproduct, we answer a question by M. P. do Carmo (see Introduction) about the leaves of such foliations
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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