Given a one-dimensional homology class in a lens space, a question related to
the Berge conjecture on lens space surgeries is to determine all knots
realizing the minimal rational genus of all knots in this homology class. It is
known that simple knots are rational genus minimizers. In this paper, we
construct many non-simple genus minimizers. This negatively answers a question
of Rasmussen.Comment: 16 pages, 6 figure
