  For projection-based linear-subspace model order reduction (MOR), it is well
known that the Kolmogorov n-width describes the best-possible error for a
reduced order model (ROM) of size n. In this paper, we provide approximation
bounds for ROMs on polynomially mapped manifolds. In particular, we show that
the approximation bounds depend on the polynomial degree p of the mapping
function as well as on the linear Kolmogorov n-width for the underlying
problem. This results in a Kolmogorov (n, p)-width, which describes a lower
bound for the best-possible error for a ROM on polynomially mapped manifolds of
polynomial degree p and reduced size n.
