Search results for "geodesics"
showing 10 items of 18 documents
Curve Extraction by Geodesics Fusion: Application to Polymer Reptation Analysis
2016
© Springer International Publishing Switzerland 2016. In the molecular field, researchers analyze dynamics of polymers by microscopy: several measurements such as length and curvature are performed in their studies. To achieve correct analysis they need to extract the curve representing as good as possible the observed polymer shape which is a grayscale thick curve with noise and blur. We propose, in this paper, a method to extract such a curve. A polymer chain moves in a snake-like fashion (Reptation): it can self-intersect and form several complex geometries. To efficiently extract the different geometries, we generate the curve by computing a piecewise centerline browsing the shape by ge…
Our Friend and Mathematician Karl Strambach
2020
This paper is dedicated to Karl Strambach on the occasion of his 80th birthday. Here we want to describe our work with Prof. Karl Strambach.
Corners in non-equiregular sub-Riemannian manifolds
2014
We prove that in a class of non-equiregular sub-Riemannian manifolds corners are not length minimizing. This extends the results of (G.P. Leonardi and R. Monti, Geom. Funct. Anal. 18 (2008) 552-582). As an application of our main result we complete and simplify the analysis in (R. Monti, Ann. Mat. Pura Appl. (2013)), showing that in a 4-dimensional sub-Riemannian structure suggested by Agrachev and Gauthier all length-minimizing curves are smooth. Mathematics Subject Classification. 53C17, 49K21, 49J15.
X-ray transforms in pseudo-Riemannian geometry
2016
We study the problem of recovering a function on a pseudo-Riemannian manifold from its integrals over all null geodesics in three geometries: pseudo-Riemannian products of Riemannian manifolds, Minkowski spaces and tori. We give proofs of uniqueness anc characterize non-uniqueness in different settings. Reconstruction is sometimes possible if the signature $(n_1,n_2)$ satisfies $n_1\geq1$ and $n_2\geq2$ or vice versa and always when $n_1,n_2\geq2$. The proofs are based on a Pestov identity adapted to null geodesics (product manifolds) and Fourier analysis (other geometries). The problem in a Minkowski space of any signature is a special case of recovering a function in a Euclidean space fro…
Prescribing the behaviour of geodesics in negative curvature
2010
Given a family of (almost) disjoint strictly convex subsets of a complete negatively curved Riemannian manifold M, such as balls, horoballs, tubular neighborhoods of totally geodesic submanifolds, etc, the aim of this paper is to construct geodesic rays or lines in M which have exactly once an exactly prescribed (big enough) penetration in one of them, and otherwise avoid (or do not enter too much in) them. Several applications are given, including a definite improvement of the unclouding problem of [PP1], the prescription of heights of geodesic lines in a finite volume such M, or of spiraling times around a closed geodesic in a closed such M. We also prove that the Hall ray phenomenon desc…
Failure of topological rigidity results for the measure contraction property
2014
We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0,3) and contains a subset isometric to $\mathbb{R}$, but does not topologically split. The second space satisfies MCP(2,3) and has diameter $\pi$, which is the maximal possible diameter for a space satisfying MCP(N-1,N), but is not a topological spherical suspension. The latter example gives an answer to a question by Ohta.
On the Uniqueness of the Energy and Momenta of an Asymptotically Minkowskian Space-Time: The Case of the Schwarzschild Metric
2013
Some theorems about the uniqueness of the energy of asymptotically Minkowskian spaces are recalled. The suitability of almost everywhere Gauss coordinates to define some kind of physical energy in these spaces is commented. Schwarzschild metric, when its source radius is larger than the Schwarzschild radius and in the case of a black hole, is considered. In both cases, by using a specific almost everywhere Gaussian coordinate system, a vanishing energy results. We explain why this result is not in contradiction with the quoted theorems. Finally we conclude that this metric is a particular case of what we have called elsewhere a creatable universe.
Schwarzschild Interior in Conformally Flat Form
2004
A unified conformally flat form of the static Schwarzschild interior space–times is provided. A new parameter that allows us to analyze the symmetry (spherical, plane or hyperbolic) of the three well known classes of metrics is introduced. In the spherically symmetric case, this parameter is related to the historical limit value of the mass to radius ratio found by Schwarzschild for a sphere of incompressible fluid.
An intrinsic characterization of the Schwarzschild metric
1998
An intrinsic algorithm that exclusively involves conditions on the metric tensor and its differential concomitants is presented to identify every type-D static vacuum solution. In particular, the necessary and sufficient explicit and intrinsic conditions are given for a Lorentzian metric to be the Schwarzschild solution.
Lens Effect and CMB Anisotropies: Deviations from Gaussianity
2003
The CMB sky can be seen as the superimposition of two components, one of them is the temperature distribution in the absence of lensing and the other one is the correction caused by lensing. In the model under consideration, the first of these components is Gaussian, but the second is not. Numerical methods to calculate angular correlations in the lens component are designed and tested. Some of these correlations are estimated. Deviations from Gaussianity are confirmed.