| Résume |
- Minimal and constant mean curvature (CMC) surfaces in all space forms belong to the wider class of isothermic surfaces. The latter are characterized by the existence of conformal curvature line coordinates. Controlling global properties of general isothermic surfaces is a challenging and often a hopeless endeavour. However, the additional requirement of a family of spherical curvature lines has proven helpful in this regard and has produced many notable examples. These include Wente tori, free boundary/capillary minimal and CMC solutions, as well as isothermic tori leading to compact Bonnet pairs.
In this talk, we will present a novel construction method for isothermic surfaces foliated by a family of spherical curvature lines. This method, called lifted-folding, allows to generate these surfaces from specific holomorphic maps, providing good control over certain global properties. The presented ideas are applicable to discrete and smooth surfaces.
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