On the area of minimal surfaces in a slab

Jaigyoung Choe (1) , Benoit Daniel (2)

1 KIAS - Korean Institute of Advanced Studies
2 IECL - Institut Élie Cartan de Lorraine

Consider a non-planar orientable minimal surface Σ in a slab which is possibly with genus or with more than two boundary components. We show that there exists a catenoidal waist W in the slab whose flux has the same vertical component as Σ such that Area(Σ) ≥ Area(W), provided the intersections of Σ with horizontal planes have the same orientation.

Domaines: Mathématiques [math]

Jaigyoung Choe, Benoit Daniel. On the area of minimal surfaces in a slab. International Mathematics Research Notices, 2016, 2016 (23), pp.7201-7211. ⟨10.1093/imrn/rnv386⟩. ⟨hal-01280463⟩