Auckly D., Sadun L.
A Family of Mobius Invariant 2-Knot Energies
(51K, AMS-TeX)

ABSTRACT.  After reviewing energy functionals for 1-dimensional knots and links,
we define a family of \Mob invariant energy functionals $E_s$
for surfaces embedded in $\real^n$.  These functionals are all finite
for smoothly embedded compact surfaces and infinite for self-intersecting
immersed surfaces.  They treat disconnected surfaces and connected sums of
surfaces correctly.  For sufficiently negative $s$, $E_s$ is  not bounded
from below.  For sufficiently positive $s$, the evidence to date suggests
that $E_s$ {\it is} bounded from below, but we have not yet found a proof.
We also discuss alternate methods of defining surface energy.