# Upper bounds for the copula density?

The Fréchet–Hoeffding upper bound applies to the copula distribution function and it is given by

$$C(u_1,…,u_d)\leq \min\{u_1,..,u_d\}.$$

Is there a similar (in the sense that it depends on the marginal densities) upper bound for the copula density $c(u_1,…,u_d)$ instead of the CDF?

Any reference would be greatly appreciated.