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Pré-Publication, Document De Travail Année : 2022

Viterbo's spectral bound conjecture for homogeneous spaces

Résumé

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.

Dates et versions

hal-03621652 , version 1 (28-03-2022)

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Stephane Guillermou, Nicolas Vichery. Viterbo's spectral bound conjecture for homogeneous spaces. 2022. ⟨hal-03621652⟩
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