4 papers
Polarization problems and Coxeter systems
Ãngel D. MartÃnez, 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, Ãngel D. MartÃnez
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
Ãngel D. MartÃnez
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 isomet…
An abstract generalization of Källen-Kröner's interation
Ãngel D. MartÃnez
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.