Ricerche di Matematica ( IF 0.970 ) Pub Date : 2020-08-01 , DOI: 10.1007/s11587-020-00533-5 Anastasia V. Vikulova
In this paper we show how the method of parallel coordinates can be extended to three dimensions. As an application, we prove the conjecture of Antunes et al. (Adv Calc Var 10:357–380, 2017) that “the ball maximises the first Robin eigenvalue with negative boundary parameter among all convex domains of equal surface area” under the weaker restriction that the boundary of the domain is diffeomorphic to the sphere and convex or axiconvex. We also provide partial results in arbitrary dimensions.