Monthly Archives: June 2019

In previous tutorials we compute immersed minimal surfaces. These immersions were the critical points of Dirichlet energy. You have seen in the lecture that, if we additionally include a volume constraint, then the critical points have no longer mean curvature … Continue reading →

Let \(M\) be a Riemannian surface and let \(\Delta\colon C^\infty M \to C^\infty M\) denote the corresponding Laplace operator. The second order linear partial differential equation \[\ddot{u} = \Delta u\]is called the wave equation and—as the name suggests—describes the motion of … Continue reading →

We are back at minimal surfaces in \(\mathbb S^3\). This time the goal is to visualize minimal surfaces in \(\mathbb S^3\) first described by Lawson, which are constructed by reflections and rotations of a fundamental piece which is a minimal … Continue reading →

As described in the lecture a charge distribution \(\rho\colon \mathrm M \to \mathbb R\) in a uniformly conducting surface \(M\) induces an electric field \(E\), which satisfies Gauss’s and Faraday’s law\[\mathrm{div}\,E = \rho, \quad \mathrm{curl}\, E = 0.\]In particular, on a simply … Continue reading →