Maximin utility function If someone has the attitude that they want to maximize their worst possible outcome (so they are maximally risk-averse), what does the utility function for that look like?  Can this attitude be expressed as a utility function?

Maybe as a function defined by a limit?
You can simply apply what you know about perfect complements. If we have $C_i$ for $i=1,2,...,n$, where $C_i$ is consumption in the $i$th state of the world, each state of the world occuring with some probability, the utility function $U=\min\{C_1,C_2,...,C_n\}$ will ensure that the consumer will choose to have equal consumption in every state of the world.