What is the equation for the optimal kink?

International conference at the Albert Einstein Institute is devoted to new mathematical methods.

June 28, 2012

Around 70 participants from all over the world are expected at the conference on Geometric Measure Theory on July 2-4, 2012.

Sometimes it takes a while for a hunch to be confirmed. For example, the English mathematician Thomas J. Willmore (1919-2005) already postulated in 1965 that certain geometrical surfaces are optimally energetic. Such investigations are important in order to be able to understand nature (which always strives for a minimum of energy) and ultimately to develop applications therefrom. The applications range from architecture to the design of new materials with a complex surface structure. This is because optimal surfaces not only play a decisive role in geometry, but also in mathematical models of material sciences.

For a long time the “Willmore Presumption” could not be proven mathematically. Yet at the beginning of this year the two mathematicians Fernando C. Marques and André Neves presented proof thereof. “At crucial points their work is based on the results of geometric measure theory. At our conference Fernando Marques will explain the proof,” according to Professor Dr. Ulrich Menne, one of the organizers of the conference. “Some geometrical equations allow for solutions that manifest ‘kinks’” and other so-called singularities. These situations can be especially well described with GMT.”

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