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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 Geometric Analysis and Partial Differential Equations seminar series.

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