ИСТИНА

An eigenvalue of the Laplace-Beltrami operator on a compact surface could be considered as a functional on the space of Riemannian metrics of fixed volume. The question about metrics extremal for this functional goes back to 70-80's pioneering works by Hersch, Yau et al and turns out to be very difficult. Recent developments in this area show an interesting interplay between minimal surfaces, classical equations of mathematical physics and group actions.