8 papers
Polarization problems and Coxeter systems
Ángel D. Martínez, Oscar Ortega-Moreno
In this paper we provide a proof of the strong polarization conjecture due to Ball and Frenkel. We observe that Coxeter systems produce unexpected new examples of extremizers. Furt…
On monotonicity of heat kernels: a new example and counterexamples
Almut Burchard, Ángel D. Martínez
We discover a new, non-radial example of a manifold whose heat kernel decreases monotonically along all minimal geodesics. We also classify the flat tori with this monotonicity pro…
Isometric embeddings
Ángel D. Martínez
In this paper we use the convex integration technique enhanced by an extra iteration originally due to Källén and revisited by Kröner to provide a local -principle for isometric…
An abstract generalization of Källen-Kröner's interation
Ángel D. Martínez
We devote this paper to provide an abstract generalization of an iteration originally due to Källén, and revisited later by Kröner, that might be of independent interest.
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…