Transverse Rigidity is Prestress Stability

TL;DR

This paper demonstrates that the recently proposed concept of transverse rigidity is equivalent to the well-established notion of prestress stability, providing a new interpretation of the prestress condition in rigidity theory.

Contribution

The paper establishes the equivalence between transverse rigidity and prestress stability, offering a novel perspective on the prestress condition in rigidity theory.

Findings

Transverse rigidity is equivalent to prestress stability.

Provides a new interpretation of prestress stability.

Bridges recent and classical rigidity concepts.

Abstract

Recently, V. Alexandrov proposed an intriguing sufficient condition for rigidity, which we will call "transverse rigidity". We show that transverse rigidity is actually equivalent to the known sufficient condition for rigidity called "prestress stability". Indeed this leads to a novel interpretation of the prestress condition.