Nonexistence of large nuclei in the liquid drop model
  We give a simplified proof of the nonexistence of large nuclei in the liquid drop model and provide an explicit bound. Our bound is within a factor of 2.3 of the conjectured value and seems to be the first quantitative result. 
Rupert L. Frank, Rowan Killip, Phan Th\`anh Nam
math-ph math.AP math.MP