Search results for " Geometry"
showing 10 items of 2294 documents
Curve packing and modulus estimates
2018
A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in $\mathbb{R}^{2}$ of length one. The classical "worm problem" of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family has always area at least $c$ for some small absolute constant $c > 0$. We strengthen Marstrand's result by showing that for $p > 3$, the $p$-modulus of a Moser family of curves is at least $c_{p} > 0$.
A Quantitative Analysis of Metrics on Rn with Almost Constant Positive Scalar Curvature, with Applications to Fast Diffusion Flows
2017
We prove a quantitative structure theorem for metrics on $\mathbf{R}^n$ that are conformal to the flat metric, have almost constant positive scalar curvature, and cannot concentrate more than one bubble. As an application of our result, we show a quantitative rate of convergence in relative entropy for a fast diffusion equation in $\mathbf{R}^n$ related to the Yamabe flow.
Some notes on a superlinear second order Hamiltonian system
2016
Variational methods are used in order to establish the existence and the multiplicity of nontrivial periodic solutions of a second order dynamical system. The main results are obtained when the potential satisfies different superquadratic conditions at infinity. The particular case of equations with a concave-convex nonlinear term is covered.
Geometry and quasisymmetric parametrization of Semmes spaces
2014
We consider decomposition spaces R/G that are manifold factors and admit defining sequences consisting of cubes-with-handles. Metrics on R/G constructed via modular embeddings of R/G into Euclidean spaces promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric space R/G×R by R for any m ≥ 0 imposes quantitative topological constraints, in terms of the circulation and the growth of the cubes-with-handles, to the defining sequences for R/G. We give a necessary condition and a sufficient condition for the existence of parametrization. The necessary condition answers negatively a question of Heinonen and Semmes on quasisymmetric parametrizabi…
Relativistic simultaneity and causality
2005
We analyze two types of relativistic simultaneity associated to an observer: the spacelike simultaneity, given by Landau submanifolds, and the lightlike simultaneity (also known as observed simultaneity), given by past-pointing horismos submanifolds. We study some geometrical conditions to ensure that Landau submanifolds are spacelike and we prove that horismos submanifolds are always lightlike. Finally, we establish some conditions to guarantee the existence of foliations in the space-time whose leaves are these submanifolds of simultaneity generated by an observer.
Poisson Geometry in Mathematics and Physics
2008
We realize quantized anti de Sitter space black holes, building Connes spectral triples, similar to those used for quantized spheres but based on Universal Deformation Quantization Formulas (UDF) obtained from an oscillatory integral kernel on an appropriate symplectic symmetric space. More precisely we first obtain a UDF for Lie subgroups acting on a symplectic symmetric space M in a locally simply transitive manner. Then, observing that a curvature contraction canonically relates anti de Sitter geometry to the geometry of symplectic symmetric spaces, we use that UDF to define what we call Dirac-isospectral noncommutative deformations of the spectral triples of locally anti de Sitter black…
Non-supersymmetric black-hole solutions in N=2,D=4 supergravity
2013
254 páginas. Tesis Doctoral del Departamento de Física Teórica, de la Universidad de Valencia.
Classical and relativistic n-body problem: from Levi-Civita to the most advanced interplanetary missions
2022
The n-body problem is one of the most important issue in Celestial Mechanics. This article aims to retrace the historical and scientific events that led the Paduan mathematician, Tullio Levi-Civita, to deal with the problem first from a classic and then a relativistic point of view. We describe Levi-Civita's contributions to the theory of relativity focusing on his epistolary exchanges with Einstein, on the problem of secular acceleration and on the proof of Brillouin's cancellation principle. We also point out that the themes treated by Levi-Civita are very topical. Specifically, we analyse how the mathematical formalism used nowadays to test General Relativity can be found in Levi-Civita'…
DETERMINANTS OF DNA METHYLATION BASED AGE ACCELERATION IN YOUNG AND OLDER TWIN PAIRS
2017
DNA methylation (DNAm) age, a novel marker of biological aging, has been shown to predict mortality and to be associated with physiological aging. However, the relative contribution of genetic and environmental factors to DNAm age over life span is not fully known. We estimated the magnitude of genetic and environmental factors in DNAm based age acceleration.
Non-equivariant cylindrical contact homology
2013
It was pointed out by Eliashberg in his ICM 2006 plenary talk that the integrable systems of rational Gromov-Witten theory very naturally appear in the rich algebraic formalism of symplectic field theory (SFT). Carefully generalizing the definition of gravitational descendants from Gromov-Witten theory to SFT, one can assign to every contact manifold a Hamiltonian system with symmetries on SFT homology and the question of its integrability arises. While we have shown how the well-known string, dilaton and divisor equations translate from Gromov-Witten theory to SFT, the next step is to show how genus-zero topological recursion translates to SFT. Compatible with the example of SFT of closed …