The paper proves a linear volume lower bound for codimension two minimal submanifolds of compact octonionic hyperbolic manifolds, yielding linear waists, systolic freedom, and new lattice fixed point theorems.
Overlap properties of geometric expanders.Journal für die reine und angewandte Mathematik (Crelles Journal), 2012(671):49–83,
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Minimal Submanifolds and Waists of Locally Symmetric Spaces
The paper proves a linear volume lower bound for codimension two minimal submanifolds of compact octonionic hyperbolic manifolds, yielding linear waists, systolic freedom, and new lattice fixed point theorems.