94-67 Auckly D., Sadun L.

A Family of Mobius Invariant 2-Knot Energies (51K, AMS-TeX) Mar 21, 94

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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.

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