Algebraic estimates , stability of local zeta functions , and uniform estimates for distribution functions

  title={Algebraic estimates , stability of local zeta functions , and uniform estimates for distribution functions},
  author={Duong H. Phong and Jacob Sturm},
A method of “algebraic estimates” is developed, and used to study the stability properties of integrals of the form ∫ B |f(z)| −δdV , under small deformations of the function f . The estimates are described in terms of a stratification of the space of functions {R(z) = |P (z)|ε/|Q(z)|δ} by algebraic varieties, on each of which the size of the integral of R(z) is given by an explicit algebraic expression. The method gives an independent proof of a result on stability of Tian in 2 dimensions, as… CONTINUE READING
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