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

TL;DR

This paper establishes sharp lower bounds for energy functionals of mappings from projective spaces to Riemannian manifolds, characterizes energy-minimizing maps, and explores connections to systolic geometry.

Contribution

It provides new sharp bounds for energy functionals and characterizes the energy-minimizing maps from projective spaces, linking geometric analysis with systolic geometry.

Findings

Lower bounds for energy functionals are sharp for real and complex projective spaces.

Characterization of the family of energy-minimizing maps.

Connections established between energy bounds and systolic geometry.

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.