ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 58, 53, 35 Ma, Li, Dept. of Applied Mathematics, Tsinghua University, Beijing, China Stable critical point Theory in perturbation problems We discuss the stable critical point theory for small perturbations of an elliptic variational functional, which is defined on a Hilbert-Riemannian manifold of functions on a finite dimensional reimannian manifold and invariant under a (non-compact) Lie group action. We use the Lyapunov-Schmidt process to reduce the problem into a finite dimensional one and give some natural conditions such that the standard bifurcation or Thom-Mather theory can be used. Our result is a complement of R. Palais’s principle of symmetrical criticality.