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A curious variational property of classical minimal surfaces

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Let $\Sigma$ be a nowhere umbilic classical minimal surface in $R^3$. We observe that the induced metric, $g$, on $\Sigma$ may be conformally deformed—in an explicit manner—to a smooth metric $\hat{g}$ which is a critical point of a natural geometric functional $\mathcal{E}$. The diffeomorphism invariance of $\mathcal{E}$ gives rise to a conservation law $T$. We characterize several important model surfaces in terms of $T$. Time permitting, the KdV equation will make an unexpected guest appearance.

This is joint work with T. Mettler.

This talk is part of the Partial Differential Equations seminar series.

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