  We study renormalization group flow of four dimensional N=2 SCFTs defined by
isolated hypersurface three-fold singularities. We define the spectrum of N=2
theory as the set of scaling dimensions of the parameters on the Coulomb
branch, which include Coulomb branch moduli, mass parameters and coupling
constants. We prove that the spectrum of those theories is semicontinous under
the RG flow on the Coulomb branch using the mathematical result about the
singularity spectra under deformation. The semicontinuity behavior of N=2
spectrum implies a theorem under relevant and Coulomb branch moduli
deformation, the absence of dangerous irrelevant deformations and can be taken
as the necessary condition for the ending point of a RG flow. This behavior is
also true for (c,c) ring deformation of two dimensional Landau-Ginzburg model
with (2,2) supersymmetry.
