Holomorphic quadratic differentials on graphs
Holomorphic quadratic differentials on graphs
In the classical theory, holomorphic quadratic differentials are tiedÌýto a wide range of objects, e.g. harmonic functions, TeichmuellerÌýÌýspace, dynamical systems and minimal surfaces. We present aÌýdiscretization of holomorphic quadratic differentials that preservesÌýsuch a rich theory.Ìý
We introduce discrete holomorphic quadratic differentials on graphs.
There arise naturally from dynamical systems, circle packings andÌýenergy minimization. We will discuss their connection to discreteÌýconformal geometry and the surface theory. On one hand, they relateÌýdiscrete harmonic functions, circle packings and Luo’s vertex scaling.Ìý
On the other hand, they unify discrete minimal surfaces via aÌýWeierstrass representation formula. Further problems will be shown inÌýthe end of the talk.
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