Instituto de Ciencias Matemáticas (ICMAT)
http://hdl.handle.net/10486/662109
2020-01-27T03:12:34ZMorphisms and period matrices
http://hdl.handle.net/10486/689464
Morphisms and period matrices
Chamizo, Fernando
Bounding the number of morphisms between compact Riemann surfaces is a long standing problem coming from complex and algebraic geometry. We show that linear algebra techniques allow to improve the known results when we assume a kind of condition number bound for the period matrix.
This Accepted Manuscript will be available for reuse under a CC BY-NC-ND licence after 24 months of embargo period
2019-12-01T00:00:00ZGlobal well-posedness of critical surface quasigeostrophic equation on the sphere
http://hdl.handle.net/10486/685411
Global well-posedness of critical surface quasigeostrophic equation on the sphere
Alonso-Orán, Diego; Córdoba, Antonio; Martínez, Ángel D.
In this paper we prove global well-posedness of the critical
surface quasigeostrophic equation on the two dimensional sphere building
on some earlier work of the authors. The proof relies on an improving
of the previously known pointwise inequality for fractional laplacians as
in the work of Constantin and Vicol for the euclidean setting
2018-02-22T00:00:00ZFocal radius, rigidity, and lower curvature bounds
http://hdl.handle.net/10486/684726
Focal radius, rigidity, and lower curvature bounds
Guijarro, Luis; Wilhelm, Frederick
We prove a new comparison lemma for Jacobi fields that exploits Wilking's transverse Jacobi equation. In contrast to standard Riccati and Jacobi comparison theorems, there are situations when our technique can be applied after the first conjugate point.
Using it, we show that the focal radius of any submanifold N of positive dimension in a manifold M with sectional curvature greater than or equal to 1 does not exceed π 2 . In the case of equality, we show that N is totally geodesic in M and the universal cover of M is isometric to a sphere or a projective space with their standard metrics, provided that N is closed.
Our results also hold for k th intermediate Ricci curvature, provided that the submanifold has dimension ⩾ k . Thus, in a manifold with Ricci curvature ⩾ n − 1 , all hypersurfaces have focal radius ⩽ π 2 , and space forms are the only such manifolds where equality can occur, if the submanifold is closed.
Example 4.38 and Remark 5.4 show that our results cannot be proven using standard Riccati or Jacobi comparison techniques
“This is the accepted version of the following article: Luis Guijarro and Frederick Wilhelm, Focal radius, rigidity, and lower curvature bounds, which has been published in final form at: https://doi.org/10.1112/plms.12113.”
2018-02-13T00:00:00ZSemiclassical basis sets for the computation of molecular vibrational states
http://hdl.handle.net/10486/679266
Semiclassical basis sets for the computation of molecular vibrational states
Revuelta, F.; Vergini, E. G.; Benito, R.M.; Borondo, Florentino
In this paper, we extend a method recently reported [F. Revuelta et al., Phys. Rev. E 87, 042921 (2013)] for the calculation of the eigenstates of classically highly chaotic systems to cases of mixed dynamics, i.e., those presenting regular and irregular motions at the same energy. The efficiency of the method, which is based on the use of a semiclassical basis set of localized wave functions, is demonstrated by applying it to the determination of the vibrational states of a realistic molecular system, namely, the LiCN molecule
2017-01-05T00:00:00Z