| Résume | The first part of the talk is dedicated to Nash's isometric embedding theorem for
surfaces. We recall the impressive results obtained by HEVEA's project for the
flat torus (V. Borrelli, F. Lazarus, B. Thibert et al.) and illustrate how spectral
formulation may lead to a new intrinsic approach which are not related to
Gromov's construction.
Following the theoretical results of Fraser and Schoen, we describe in a second
part a numerical approach to approximate minimal surfaces in the ball that is
surfaces (i) contained in the ball (ii) that have zero mean curvature and (ii)
meet the boundary of the ball orthogonally.
For genus γ = 0 and b = 2, . . . , 9, 12, 15, 20 boundary components, we
numerically solve the extremal Steklov problem for the first eigenvalue. The
corresponding eigenfunctions generate a free boundary minimal surface, which
have not been observed previously. |
