Monthly Archives: May 2019

In the lecture we have defined what we mean by a discrete minimal surface. The goal of this tutorial is to visualize such minimal surfaces. Let $\mathrm{M}$ be a discrete surface with boundary and let $V,E,F$ denote the set of vertices, … Continue reading →

In the lecture we saw that the Dirichlet energy has a unique minimizer among all functions with prescribed boundary values. In this tutorial we want to visualize these minimizers in the discrete setting. Let $\mathrm{M}\subset {\mathbb{R}}^2$ be a triangulated surface … Continue reading →

Let $M\subset \mathbb{C}$ be an open set and $V$ a complex vector space with a non-degenerated complex-valued symmetric complex-bilinear form $⟨.,.⟩$. A null-curve is a map $\gamma :M\to V$ such that$${\gamma }^{\ast }⟨.,.⟩=⟨d\gamma ,d\gamma ⟩=0.$$Unless explicitly stated … Continue reading →

The real projective plane $\mathbb{R}{\mathrm{P}}^2$ is obtained by identifying the antipodal points of the a $2$-sphere ${\mathbb{S}}^2$, i.e. $\mathbb{R}{\mathrm{P}}^2={\mathbb{S}}^2{/}_{\sim }$ with equivalence relation given by $$x\sim y\iff y=\pm x.$$ The … Continue reading →