On the first twisted Dirichlet eigenvalue

Pedro Freitas (1) , Antoine Henrot (2)

1 DM/IST - Departamento de Matemática [Lisbonne]
2 CORIDA - Robust control of infinite dimensional systems and applications

In this paper we prove an isoperimetric inequality for the twisted Dirichlet eigenvalue which was introduced by Barbosa and B\'{e}rard in the context of constant mean curvature surfaces. More precisely, we show that in the Euclidean case this eigenvalue is minimized by the union of two equal balls.

Domaines: Equations aux dérivées partielles [math.AP]

Pedro Freitas, Antoine Henrot. On the first twisted Dirichlet eigenvalue. Communications in Analysis and Geometry, 2004, 12, pp.1083-1103. ⟨hal-00014216v2⟩