For compact rank one symmetric spaces, string point invertibility over a field of characteristic p holds exactly when p equals the Euler characteristic, and the same condition yields uniform resonance bounds on critical levels of loop homology classes.
Viterbo's spectral bound conjecture for homogeneous spaces
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abstract
We prove a conjecture of Viterbo about the spectral distance on the space of compact exact Lagrangian submanifolds of a cotangent bundle $T^*M$ in the case where $M$ is a compact homogeneous space: if such a Lagrangian submanifold is contained in the unit ball bundle of $T^*M$, its spectral distance to the zero section is uniformly bounded. This also holds for some immersed Lagrangian submanifolds if we take into account the length of the maximal Reeb chord.
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Resonances and string point invertibility for compact rank one symmetric spaces
For compact rank one symmetric spaces, string point invertibility over a field of characteristic p holds exactly when p equals the Euler characteristic, and the same condition yields uniform resonance bounds on critical levels of loop homology classes.