On variational problems related to steepest descent curves and self dual convex sets on the sphere

Marco Longinetti, Paolo Manselli, Adriana Venturi

Let $\mathcal{C}$ be the family of compact convex subsets $S$ of the hemisphere in $\rn$ with the property that $S$ contains its dual $S^{\ast };$ let $u\in S^{\ast }$, and let $ Φ(S,u)=\frac{…