Let $\mathcal{F}_1,\mathcal{F}_2$ torsion-free coherent sheaves on a smooth, projective, irreducible, reduced scheme $X$ (id est, $X$ is a smooth projective variety) of dimension $n\geq1$ over an algebraically closed field $\mathbb{K}$ of characteristic $0$.
One defines the slope of $\mathcal{F}_k$ as $\displaystyle\mu(\mathcal{F}_k)=\frac{\deg(\mathcal{F}_k)}{\text{rank}(\mathcal{F}_k)}\in\mathbb{Q}$.
$\mathcal{F}_k$ is semistable (respectively, stable) if $\mu(\mathcal{E})\leq\mu(\mathcal{F}_k)$ (respectively, $\mu(\mathcal{E})<\mu(\mathcal{F}_k)$) for every torsion-free subsheaf $\mathcal{E}$ of $\mathcal{F}_k$ with $0<\text{rank}(\mathcal{E})<\text{rank}(\mathcal{F}_k)$.
There exist unique filtrations (the Harder-Narasimhan filtration of $\mathcal{F}_k$) \begin{equation} \{0\}=\mathcal{E}_{k,0}\subset\mathcal{E}_{k,1}\subset\dotsc\subset\mathcal{E}_{k,s_k-1}\subset\mathcal{E}_{k,s_k}=\mathcal{F}_k \end{equation} such that $\forall j\in\{1,\dotsc,s_k\},\,\mathcal{E}_{k,j}/\mathcal{E}_{k,j-1}$ is semistable of slope $\mu_{j,k}$ and $\mu_{\max}(\mathcal{F}_k)=\mu_{k,1}>\dotsc>\mu_{k,s_k}=\mu_{\min}(\mathcal{F}_k)$.
It is possible to prove that $\mathcal{E}_{k,1}$ is the semistable subsheaf of $\mathcal{F}_k$ with maximal slope and rank (see proof of [b, Theorem 12]).
Where $k\in\{1,2\}$!
At page 29 of [a], I read that $\mu_{\min}(\mathcal{F}_1\otimes\mathcal{F}_2)\leq\mu_{\min}(\mathcal{F}_1)+\mu_{\min}(\mathcal{F}_2)$ and $\mu_{\max}(\mathcal{F}_1\otimes\mathcal{F}_2)\leq\mu_{\max}(\mathcal{F}_1)+\mu_{\max}(\mathcal{F}_2)$. But $\mathcal{E}_{1,1}\otimes\mathcal{E}_{2,1}$ is a subsheaf of $\mathcal{F}_1\otimes\mathcal{F}_2$ and therefore $\mu_{\min}(\mathcal{F}_1\otimes\mathcal{F}_2)\geq\mu(\mathcal{E}_{1,1}\otimes\mathcal{E}_{2,1})=\mu_{\min}(\mathcal{F}_1)+\mu_{\min}(\mathcal{F}_2)$.
Am I wrong? Or is this a misprinting in [a]?
[a] D. Huybrechts, M. Lehn (2010) The Geometry of Moduli Spaces of Sheaves. Second Edition, Cambridge University Press.
[b] J. Lurie (11/19/2018) The Harder-Narasimhan Filtration.