| Résume | Lawson proved that closed surfaces of any orientable topological type can be embedded as a minimal surface in the three-dimensional round
sphere. In higher-dimensional spheres however, little is known about the possible topological types of minimal hypersurfaces.
We prove that the four-dimensional round sphere contains a minimally embedded hypertorus, as well as infinitely many, pairwise non-isometric,
immersed ones. Our analysis also yields infinitely many, pairwise non-isometric, minimally embedded hyperspheres and thus provides a self-contained
solution to Chern's spherical Bernstein conjecture in dimension four.
Joint work with A Carlotto. |
