Vanishing Cycles and the Inverse Problem of Potential Theory

Details Vanishing Cycles and the Inverse Problem of Potential Theory Vanishing Cycles and the Inverse Problem of Potential Theory

2001-11-11

arxiv.org/abs/math/0111129v1

Mathematics

Differential Geometry

Scientific paper

In this paper we prove the infinitesimal uniqueness theorem for the Newton potential of non simply connected bodies using the singularity theory approach. We consider the Newtonian potentials of the domains in ${\bf R}^n$ boundaries of which are the vanishing cycles on the level hypersurface of a holomorphic function with isolated singularity at 0. These domains don't have to be convex, connected or simply connected, we also don't have any dimensional restrictions. We consider multiparametric families of such domains in the miniversal deformation of the original function. We show that in the parameter space any point has a neighborhood s.t. potentials of the domains corresponding to parameters from this neighborhood are all different as functions of the external parameter y.

Affiliated with

Also associated with

No associations

Rating

Vanishing Cycles and the Inverse Problem of Potential Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Vanishing Cycles and the Inverse Problem of Potential Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vanishing Cycles and the Inverse Problem of Potential Theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-407519