The Best Constant of Discrete Sobolev Inequality with Hamilton Path on Tetra-, Hexa- and Octa- Polyhedra

Abstract

Abstract. We consider a classical mechanical model of tetra-, hexa- and octa- polyhedra. Its neighboring two atoms are connected with a linear spring, whose constant is different between the case with Hamilton path and the case without Hamilton path. The discrete Sobolev inequality shows that the maximum of deviation is estimated from constant multiples of the potential energy. Hence, it is expected that the best constant represents the rigidity of the mechanical model.