Title Discrete zero mean curvature surfaces in Lorentz-Minkowski 3-space
Abstract:
In the smooth case, spacelike maximal surfaces (spacelike surfaces with vanishing mean curvature) and timelike minimal surfaces (timelike surfaces with vanishing mean curvature) admit Weierstrass-type representations in terms of certain holomorphicity. These representations for smooth surfaces are powerful tools for constructing surfaces and analyzing their behaviors. By the same reason, Weierstrass-type representations for discrete surfaces are important both for exploring the discrete surface theory itself and for expanding our knowledge of behaviors of discrete surfaces.
In this talk we mainly focus on zero mean curvature surfaces in Lorentz-Minkowski 3-space. We introduce Weierstrass-type representations for discrete zero mean curvature surfaces in Lorentz-Minkowski 3-space, and analyze their behaviors. In the smooth case, spacelike maximal and timelike minimal surfaces generally have singularities, so it is expected that configurations of singularities also appear in the discrete case. We introduce our analysis on their singularities. If time allows, we introduce further development in this direction (joint work with Mason Pember and Denis Polly).