I am interested in vector bundles over a nonsingular complete algebraic curve $C$ over $\mathbb C$. For a vector bundle $E$, its Harder-Narasimhan filtration is a filtration of subbundles $$0=E_0\subset E_1\subset\cdots\subset E_n=E$$ such that each $E_i/E_{i-1}$ is semitable and $\frac{\deg(E_1/E_0)}{\mathrm{rank}(E_1/E_0)}>\cdots>\frac{\deg(E_n/E_{n-1})}{\mathrm{rank}(E_n/E_{n-1})}$.

Now if we have two vector bundles $E,F$ and we know their HN filtation $\{E_i\},\{F_j\}$, can we get any information about the HN filtration of $E\otimes F$?

One information I am interested in is the upper bound of $\frac{\deg}{\mathrm{rank}}$ of subbundles of $E\otimes F$.

Thanks.