Zobrazeno 1 - 10
of 1 064
pro vyhledávání: '"A. Verdiere"'
Autor:
de Verdière, Éric Colin, Hliněný, Petr
The basic crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. In this paper, we develop fixed-parameter tractable (FPT) algorithms for various generalized crossing number pr
Externí odkaz:
http://arxiv.org/abs/2410.00206
Autor:
de Verdìère, Yves Colin
Publikováno v:
Quarterly journal of pure and applied mathematics, 2023, 19 (4), pp.1839--1853
In this survey paper, I describe some aspects of the dynamics and the spectral theory of sub-Riemannian3D contact manifolds. We use Toeplitz quantization of the characteristic coneas introduced by Louis Boutet de Monvel and Victor Guillemin. We also
Externí odkaz:
http://arxiv.org/abs/2409.12665
This paper is motivated by recent works on inverse problems for acoustic wave propagation in the interior of gas giant planets. In such planets, the speed of sound is isotropic and tends to zero at the surface. Geometrically, this corresponds to a Ri
Externí odkaz:
http://arxiv.org/abs/2406.19734
We initiate the study of computing shortest non-separating simple closed curves with some given topological properties on non-orientable surfaces. While, for orientable surfaces, any two non-separating simple closed curves are related by a self-homeo
Externí odkaz:
http://arxiv.org/abs/2403.11749
In geophysical environments, wave motions that are shaped by the action of gravity and global rotation bear the name of gravito-inertial waves. We present a geometrical description of gravito-inertial surface waves, which are low-frequency waves exis
Externí odkaz:
http://arxiv.org/abs/2402.12992
Pancake-like vortices are often generated by turbulence in geophysical flows. Here, we study the inertia-gravity oscillations that can exist within such geophysical vortices, due to the combined action of rotation and gravity. We consider a fluid enc
Externí odkaz:
http://arxiv.org/abs/2402.10749
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices and edges of
Externí odkaz:
http://arxiv.org/abs/2311.00437
Autor:
de Verdière, Yves Colin, Li, Zhenhao
Publikováno v:
Prob. Math. Phys. 5 (2024) 735-751
We study a model of internal waves in an effectively 2D aquarium under periodic forcing. In the case when the underlying classical dynamics has sufficiently irrational rotation number, we prove that the energy of the internal waves remains bounded. T
Externí odkaz:
http://arxiv.org/abs/2306.13834
Publikováno v:
J.Math.Anal.App. 534, 128040 (2024)
Eigenvalue spectrum of the Laplacian on a metric graph with arbitrary but fixed vertex conditions is investigated in the limit as the lengths of all edges decrease to zero at the same rate. It is proved that there are exactly four possible types of e
Externí odkaz:
http://arxiv.org/abs/2306.00631
We reprove the fact, due to Backus, that the Poincar{\'e} operator in ellipsoids admits a pure point spectrum with polynomial eigenfunctions.We then show that the eigenvalues of the Poincar{\'e} operator restricted to polynomial vector fields of fixe
Externí odkaz:
http://arxiv.org/abs/2305.01369