Stability of $C^\infty$ convex integrands
  In this paper, it is shown that the set consisting of stable convex integrands $S^n\to \mathbb{R}_+$ is open and dense in the set consisting of $C^\infty$ convex integrands with respect to Whitney $C^\infty$ topology. Moreover, an application of the proof of this result is also shown. 
Erica Boizan Batista, Huhe Han and Takashi Nishimura
math.GT