Variational Convergence of Discrete Minimal Surfaces
arXiv:1605.0528513 citationsh-index: 26
Originality Incremental advance
AI Analysis
Provides theoretical guarantees for discrete approximations of the Plateau problem, relevant to computational geometry and numerical analysis.
Proved that discrete minimal surfaces (simplicial area minimizers) converge to smooth minimal surfaces under mesh refinement, with convergence in both position and normals.
Building on and extending tools from variational analysis, we prove Kuratowski convergence of sets of simplicial area minimizers to minimizers of the smooth Douglas-Plateau problem under simplicial refinement. This convergence is with respect to a topology that is stronger than uniform convergence of both positions and surface normals.