arXiv subjects

T. Bouziane

Publications and source records attributed to T. Bouziane.

2 recordsLinked to original sources

arXiv2007

Stochastic Characterization of Harmonic maps on Riemannian polyhedra

We have completely rewritten the paper, and corrected the proofs. We construct an exponential map at any point in the (n-1)-skeleton minus the (n-2)-skeleton of an n-dimensional Riemannian polyhedron. We have added allover the extra-assumption that the exponential map is totally geodesic at points in the (n-1)-skeleton minus the (n-2)-skeleton. This condition is automatically realized for instance if the dimension is one, or if the metric is flat.

math.PR↗

arXiv2004

Pseudo Harmonic Morphisms on Riemannian Polyhedra

The aim of this paper is to extend the notion of pseudo harmonic morphism (introduced by Loubeau \cite {Lo}) to the case when the source manifold is an admissible Riemannian polyhedron. We define these maps to be harmonic in the sense of Eells-Fuglede \cite {EF} and pseudo-horizontally weakly conformal in our sense (see Section 3). We characterize them by means of germs of harmonic functions on the source polyhedron, in sense of Korevaar-Schoen \cite {KS}, and germs of holomorphic functions on the Kähler target manifold.

math.DG↗