Energy-minimizing Mappings of Complex Projective Spaces
Differential Geometry
2024-11-14 v2 Algebraic Geometry
Complex Variables
Abstract
We show that in all homotopy classes of mappings from complex projective space to Riemannian manifolds, the infimum of the energy is proportional to the infimal area in the homotopy class of mappings of the 2-sphere which represents the induced homomorphism on the second homotopy group. We then establish a family of optimal lower bounds for a larger class of energy functionals for mappings from real and complex projective space to Riemannian manifolds and characterize the mappings which attain these lower bounds.
Cite
@article{arxiv.2311.08285,
title = {Energy-minimizing Mappings of Complex Projective Spaces},
author = {Joseph Hoisington},
journal= {arXiv preprint arXiv:2311.08285},
year = {2024}
}
Comments
Expository changes. v2 matches the submitted version