Upper bounds for the first dirichlet eigenvalue of a tube around an algebraic complex curve of ℂP n (λ)

摘要

We give an upper bound for the first Dirichlet eigenvalue of a tube around a complex curve P of ℂP n (λ) which depends only on the radius of the tube and the degrees of the polynomials defining P. The bound is sharp on a totally geodesic ℂP 1(λ) and gives a gap between the eigenvalue of a tube around ℂP 1(λ) and around other complex curves.