Asymptotic estimates of holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds

Abstract

Let M be a projective manifold and L be an ample line bundle over M with a Hermitian metric h whose Chern form is a Kähler form ω. Let X ⊂ M be a Lagrangian submanifold of (M, ω). When X satisfies the Bohr-Sommerfeld condition, we give an asymptotic estimate of the norm |f | h k on X for f ∈ H 0 (M, L k ).