Nikolai Nadirashvili
Berger's Isoperimetric Problem and Minimal Immersions of Surfaces
The paper is published: Geom. Funct. Anal. 6, 5 (1996) 877-897

MSC:

58G25 Spectral problems; spectral geometry; scattering theory, See also {35Pxx}

Abstract: We establish an isoperimetric inequality for the first non-zero
eigenvalue of the Laplace operator on the surface of genus one and of
a fixed area.

Keywords: isoperimetric inequality, Laplace operator, surface of genus one, Berger's problem