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Given an exact Lagrangian $L$ of an exact symplectic manifold $(M,d\lambda)$, Cornea and Shelukhin recently introduced a remarkable "cobordism metric"$d_c$ on the exact Lagrangian cobordism class $\mathcal{L}(L)$ of $L$. In thisnote we show that the Liouville flow of $(M,d\lambda )$ induces a flow on$(\mathcal{L}(L),d_c)$ which expands cobordism distances. In particular wededuce that $(\mathcal{L}(L),d_c)$ has infinite diameter whenever the Liouvilleflow is complete. We also discuss (Hamiltonian and Lagrangian) Hofer-geometricversions of our result. The proof only uses elementary differential geometry.

A distance expanding flow on exact Lagrangian cobordism classes