Rigidity of Lagrangian embeddings into symplectic tori and K3 surfaces

Michael Entov, Misha Verbitsky

Research output: Contribution to journalArticlepeer-review


A Kähler-type form is a symplectic form compatible with an integrable complex structure. Let be either a torus or a K3-surface equipped with a Kähler-type form. We show that the homology class of any Maslov-zero Lagrangian torus in has to be nonzero and primitive. This extends previous results of Abouzaid and Smith (for tori) and Sheridan and Smith (for K3-surfaces) who proved it for particular Kähler-type forms on. In the K3 case, our proof uses dynamical properties of the action of the diffeomorphism group of on the space of the Kähler-type forms. These properties are obtained using Shah's arithmetic version of Ratner's orbit closure theorem.

Original languageEnglish
Pages (from-to)8964-9000
Number of pages37
JournalInternational Mathematics Research Notices
Issue number10
StatePublished - 1 May 2023

ASJC Scopus subject areas

  • General Mathematics


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