Complex zeros of real ergodic eigenfunctions

• 成果类型: Article
• 署名作者: Zelditch, Steve
• 署名单位: Johns Hopkins University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-006-0024-z
• 发表日期: 2007
• 页码: 419-443
• 关键词: grauert tubes; subprincipal terms; tangent bundle; equation; MANIFOLDS

摘要

We determine the limit distribution (as lambda -> infinity) of complex zeros for holomorphic continuations p(lambda)(C) to Grauert tubes of real eigenfunctions of the Laplacian on a real analytic compact Riemannian manifold (M, g) with ergodic geodesic flow. If {p(jk)} is an ergodic sequence of eigenfunctions, we prove the weak limit formula 1/lambda j [Z(pjk)(C)] -> i/pi partial derivative partial derivative vertical bar xi vertical bar(g), where [Z(pjk)(C)] is the current of integration over the complex zeros and where. is with respect to the adapted complex structure of Lempert-Szoke and Guillemin-Stenzel.