Asymptotic estimates of holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds

Abstract

Let $M$ be a complex manifold and $L$ be a line bundle over $M$ with a Hermitian metric $h$ whose Chern form is a Kähler form $\omega$. Let $X\subset M$ be a Lagrangian submanifold of $(M,\omega )$. When $X$ satisfies the Bohr-Sommerfeld condition, we give an asymptotic estimate of the norm $|f{|}_{h^k}$ on $X$ for $f\in H^0(M,L^k)$.

arXiv commentThis version, to appear in Kodai Math. J., includes substantial improvements in exposition and corrections of several errors and typos