Arnold's seminar -- October 19, 1999

G. Karpunin

"Analog of Morse theory for planar linear networks and
 the generalised Steiner problem"

 The generalised Steiner problem is to discribe all locally minimal
networks spanning a given set on a plane. For solving this problem we
propose to use the analog of Morse theory for planar linear networks
spannining a given boundary set. This analog will be presented.
The results of this theory are helpfull for finding some estimates on the
number of all locally minimal networks spanning a given boundary set.