4 papers · 1 filter
On the blow up of a non-local transport equation in compact manifolds
Diego Alonso-Orán, Ángel D. Martínez
In this note we show finite time blow-up for a class of non-local active scalar equations on compact Riemannian manifolds. The strategy we follow was introduced by Silvestre and Vi…
Córdoba's differentation theorem: revisited
Ángel D. Martínez
In this paper we prove an exponential covering lemma implying the three dimensional case of a well-known conjecture formulated by A. Zygmund circa 1935 and solved by A. Córdoba in…
Distribution symmetry of toral eigenfunctions
Ángel D. Martínez, Francisco Torres de Lizaur
In this paper we study a number of conjectures on the behavior of the value distribution of eigenfunctions. On the two dimensional torus we observe that the symmetry conjecture hol…
Eigenfunction maxima and spherical means
Ángel D. Martínez
The eigenfunctions of the Laplacian are a central object from the realms of analytic number theory to geometric analysis. We prove that Hörmander - estimates are e…