Calibrations and Energy-Minimizing Mappings of Rank-1 Symmetric Spaces

Abstract

We prove lower bounds for energy functionals of mappings from real, complex and quaternionic projective spaces to Riemannian manifolds. For real and complex projective spaces, these lower bounds are sharp, and we characterize the family of energy minimizing maps which arise in these results. We discuss the connections between these results and several theorems and questions in systolic geometry.

arXiv commentTheorems 1.1, 1.2, 1.4, 4.1, and Lemma 2.4 are subsumed by results in arXiv:2311.08285. Note that arXiv:2311.08285 and v3 of this preprint also correct a misstatement in earlier versions of Theorems 1.2, 1.4, 4.1, and Lemma 2.4. The other results in this preprint are also subsumed by work which is currently in preparation. We retain this preprint as a temporary reference for these results