Given an element in the first homology of a rational homology 3-sphere, one can consider the minimal rational genus of all knots in this
homology class. We will give a lower bound for this minimal rational genus
using the correction terms in Heegaard Floer homology. As a corollary, we
show that Floer simple knots in L-spaces are genus minimizers in their
homology classes. This is joint work with Zhongtao Wu.