179 research outputs found
Can we make a Finsler metric complete by a trivial projective change?
A trivial projective change of a Finsler metric is the Finsler metric . I explain when it is possible to make a given Finsler metric both
forward and backward complete by a trivial projective change.
The problem actually came from lorentz geometry and mathematical relativity:
it was observed that it is possible to understand the light-line geodesics of a
(normalized, standard) stationary 4-dimensional space-time as geodesics of a
certain Finsler Randers metric on a 3-dimensional manifold. The trivial
projective change of the Finsler metric corresponds to the choice of another
3-dimensional slice, and the existence of a trivial projective change that is
forward and backward complete is equivalent to the global hyperbolicity of the
space-time.Comment: 11 pages, one figure, submitted to the proceedings of VI
International Meeting on Lorentzian Geometry (Granada
Finsler geodesics in the presence of a convex function and their applications
We obtain a result about the existence of only a finite number of geodesics
between two fixed non-conjugate points in a Finsler manifold endowed with a
convex function. We apply it to Randers and Zermelo metrics. As a by-product,
we also get a result about the finiteness of the number of lightlike and
timelike geodesics connecting an event to a line in a standard stationary
spacetime.Comment: 16 pages, AMSLaTex. v2 is a minor revision: title changed, references
updated, typos fixed; it matches the published version. This preprint and
arXiv:math/0702323v3 [math.DG] substitute arXiv:math/0702323v2 [math.DG
A note on the existence of standard splittings for conformally stationary spacetimes
Let be a spacetime which admits a complete timelike conformal Killing
vector field . We prove that splits globally as a standard
conformastationary spacetime with respect to if and only if is
distinguishing (and, thus causally continuous). Causal but non-distinguishing
spacetimes with complete stationary vector fields are also exhibited. For the
proof, the recently solved "folk problems" on smoothability of time functions
(moreover, the existence of a {\em temporal} function) are used.Comment: Metadata updated, 6 page
The causal structure of spacetime is a parameterized Randers geometry
There is a by now well-established isomorphism between stationary
4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries -
these Randers geometries being a particular case of the more general class of
3-dimensional Finsler geometries. We point out that in stably causal
spacetimes, by using the (time-dependent) ADM decomposition, this result can be
extended to general non-stationary spacetimes - the causal structure (conformal
structure) of the full spacetime is completely encoded in a parameterized
(time-dependent) class of Randers spaces, which can then be used to define a
Fermat principle, and also to reconstruct the null cones and causal structure.Comment: 8 page
Convex domains of Finsler and Riemannian manifolds
A detailed study of the notions of convexity for a hypersurface in a Finsler
manifold is carried out. In particular, the infinitesimal and local notions of
convexity are shown to be equivalent. Our approach differs from Bishop's one in
his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the
Riemannian case. Ours not only can be extended to the Finsler setting but it
also reduces the typical requirements of differentiability for the metric and
it yields consequences on the multiplicity of connecting geodesics in the
convex domain defined by the hypersurface.Comment: 22 pages, AMSLaTex. Typos corrected, references update
Predictive value of CDKN2A/p16INK4a expression in the malignant transformation of oral potentially malignant disorders: Systematic review and meta-analysis
[Abstract] Background: Management of oral potentially malignant disorders (OPMDs) is still challenging. Despite the
diagnostic ascertainment by bioptic examination, this method is poorly informative of the prognosis and subsequent
malignant transformation. Prognosis is based on histological findings by grading of dysplasia. Immunohistochemical
expression of p16INK4a has been investigated in different studies, with controversial results. In
this scenario, we systematically revised the current evidence about p16INK4a immunohistochemical expression
and the risk of malignization of OPMDs.
Material and methods: After a proper set of keywords combination, 5 databases were accessed and screened to
select eligible studies. The protocol was previously registered on PROSPERO (Protocol ID: CRD42022355931).
Data were obtained directly from the primary studies as a measure to determine the relationship between
CDKN2A/P16INK4a expression and the malignant transformation of OPMDs. Heterogeneity and publication bias
were investigated by different tools, such as Cochran’s Q test, Galbraith plot and Egger and Begg Mazumdar’s
rank tests.
Results: Meta-analysis revealed a twofold increased risk to malignant development (RR = 2.01, 95% CI =
1.36–2.96 - I2 = 0%). Subgroup analysis did not highlight any relevant heterogeneity. Galbraith plot showed that
no individual study could be considered as an important outlier.
Conclusion: Pooled analysis showed that p16INK4a assessment may arise adjunct tool to dysplasia grading, leading
to an optimized determination of the potential progression to cancer of OPMDs. The p16INK4a overexpression
analysis by immunohistochemistry techniques has a multitude of virtues that may facilitate its incorporation in
the day-to-day prognostic study of OPMDs
On the definition and examples of cones and finsler spacetimes
The authors warmly acknowledge Professor Daniel Azagra (Universidad Complutense, Madrid) his advise on approximation of convex functions as well as Profs. Kostelecky (Indiana University), Fuster (University of Technology, Eindhoven), Stavrinos (University of Athens), Pfeifer (University of Tartu), Perlick (University of Bremen) and Makhmali (Institute of Mathematics, Warsaw) their comments on a preliminary version of the article. The careful revision by the referee is also acknowledged. This work is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Region de Murcia, Spain, by Fundacion Seneca, Science and Technology Agency of the Region de Murcia. MAJ was partially supported by MINECO/FEDER project reference MTM2015-65430-P and Fundacion Seneca project reference 19901/GERM/15, Spain and MS by Spanish MINECO/ERDF project reference MTM2016-78807-C2-1-P.A systematic study of (smooth, strong) cone structures C and Lorentz–Finsler metrics L is carried out. As a link between both notions, cone triples (Ω,T,F), where Ω (resp. T) is a 1-form (resp. vector field) with Ω(T)≡1 and F, a Finsler metric on ker(Ω), are introduced. Explicit descriptions of all the Finsler spacetimes are given, paying special attention to stationary and static ones, as well as to issues related to differentiability. In particular, cone structures C are bijectively associated with classes of anisotropically conformal metrics L, and the notion of cone geodesic is introduced consistently with both structures. As a non-relativistic application, the time-dependent Zermelo navigation problem is posed rigorously, and its general solution is provided.MINECO/FEDER project, Spain
MTM2015-65430-PFundacion Seneca
19901/GERM/15Spanish MINECO/ERDF project
MTM2016-78807-C2-1-
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