Contact non-squeezing and orderability via the shape invariant.

In this paper, we prove a contact non-squeezing result for a class of embeddings between starshaped domains in the contactization of the symplectization of the unit cotangent bundle of certain manifolds. The class of embeddings includes embeddings which are not isotopic to the identity. This yields a new proof that there is no positive loop of contactomorphisms in the unit cotangent bundles under consideration. The arguments are inspired by the shape invariant introduced by Sikorav and Eliashberg. [ABSTRACT FROM AUTHOR]