Rigidity of bordered polyhedral surfaces
Geometric Topology
2023-08-17 v2
Abstract
This paper investigates the rigidity of bordered polyhedral surfaces. Using the variational principle, we show that bordered polyhedral surfaces are determined by boundary value and discrete curvatures on the interior edges. As a corollary, we reprove the classical result that two Euclidean cyclic polygons (or hyperbolic cyclic polygons) are congruent if the lengths of their sides are equal.
Keywords
Cite
@article{arxiv.2205.03606,
title = {Rigidity of bordered polyhedral surfaces},
author = {Te Ba and Shengyu Li and Yaping Xu},
journal= {arXiv preprint arXiv:2205.03606},
year = {2023}
}