  The notion of the capacity of a polynomial was introduced by Gurvits around
2005, originally to give drastically simplified proofs of the Van der Waerden
lower bound for permanents of doubly stochastic matrices and Schrijver's
inequality for perfect matchings of regular bipartite graphs. Since this
seminal work, the notion of capacity has been utilized to bound various
combinatorial quantities and to give polynomial-time algorithms to approximate
such quantities (e.g., the number of bases of a matroid). These types of
results are often proven by giving bounds on how much a particular differential
operator can change the capacity of a given polynomial. In this paper, we unify
the theory surrounding such capacity preserving operators by giving tight
capacity preservation bounds for all nondegenerate real stability preservers.
We then use this theory to give a new proof of a recent result of Csikv\'ari,
which settled Friedland's lower matching conjecture.
