Cellular harmonic maps which are not diffeomorphisms
F. T. Farrell, P. Ontaneda
TL;DR
This paper presents examples of harmonic cellular maps between negatively curved manifolds that are not diffeomorphisms but are homotopic to them, challenging assumptions about the relationship between harmonicity and diffeomorphism.
Contribution
It provides explicit examples of harmonic cellular maps that are not diffeomorphisms, expanding understanding of harmonic maps in negatively curved geometry.
Findings
Existence of harmonic cellular maps not being diffeomorphisms
These maps are homotopic to diffeomorphisms
Counterexamples to previous assumptions
Abstract
We give examples of harmonic cellular maps between negatively curved manifolds which are not diffeomorphisms but are homotopic to diffeomorphisms.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Cellular Mechanics and Interactions · Mathematical Dynamics and Fractals