Harmonic maps between ideal 2-dimensional simplicial complexes

Simplicial Energy and Simplicial Harmonic Maps

We introduce a combinatorial energy for maps of triangulated surfaces with simplicial metrics and analyze the existence and uniqueness properties of the corresponding harmonic maps. We show that some important applications of smooth harmonic maps can be obtained in this setting.

2 . 2 Simplicial Complexes

We study the homology of a filtered d-dimensional simplicial complex K as a single algebraic entity and establish a correspondence that provides a simple description over fields. Our analysis enables us to derive a natural algorithm for computing persistent homology over an arbitrary field in any dimension. Our study also implies the lack of a simple classification over non-fields. Instead, we ...

Harmonic Maps between 3 - Dimensional Hyperbolic Spaces

We prove that a quasiconformal map of the sphere S admits a harmonic quasi-isometric extension to the hyperbolic space H, thus confirming the well known Schoen Conjecture in dimension 3.

Stable Exponentially Harmonic Maps Between Finsler Manifolds

stable exponentially harmonic maps between finsler manifolds