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arXiv · 2311.08285

Energy-minimizing Mappings of Complex Projective Spaces

Joseph Hoisington
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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.

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Joseph Hoisington. 2023-11-14. Energy-minimizing Mappings of Complex Projective Spaces. https://arxiv.org/abs/2311.08285

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