If, by "h with an upper tilt", you mean $h'()$, then that notation simply means the derivative of $h()$.
If you mean $\tilde{h}(x)$, the symbol is called a "tilde." This notation isn't completely standard but is used by some authors in convex optimization to mean the extension of a function with a limited domain to all of $R^{n}$ by defining the function to be $+\infty$ if $x$ is outside of the domain. If the domain of $h$ is $D$, then in this notation:
$\tilde{h}(x)=\left\\{ \begin{array}{ll} h(x) & x \in D \\\ +\infty & x \
otin D \end{array} \right.$
Hopefully, the author of these slides defined the notation that they were using early in the presentation.