On the existence of a minimum of the integral ∫^{𝑥₁}_{𝑥₀}𝐹(𝑥,𝑦,𝑦’)𝑑𝑥 when 𝑥₀ and 𝑥₁ are conjugate points, and the geodesics on an ellipsoid of revolution: a revision of a theorem of Kneser’s
Transactions of the American Mathematical Society