Symmetric variational methods

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Suppose you are given a dirty photocopy and you need to touch it up.The human eye is very good at guessing how missing pieces of curvesshould be joined up. Now suppose you have hundreds of such copies.Can a computer do it? The problem is that we can do these thingswithout knowing how we do it. A computer has to be told exactlywhat to do, in the computer's own language. This means we needto solve the problem of curve completion using mathematics.This project is a contribution to this and similar problemswhich can be described in the same mathematical terms.Basically, we try lots of different completions and ask,which looks best? Formulating what it means to ``look best is one problem, finding a way to describe the solutionis another. The key to success is to make the solutionmethod resemble mathematics we already know and love.