Uma Caracterização do Catenoide Crítico - RODRIGUES, Bruno Pereira (2021)
The free boundary minimal surfaces embedded surfaces in the unit ball of the three- dimensional euclidean space are critical points of the functional area among embedded surfaces in B3 . The present work focuses on the results provided in the article A Cha- racterization of the Critical Catenoid by Peter McGrath [14], where he characterizes the critical catenoid as the only embedded free boundary minimal annulus in the unit ball at R 3 invariant by reflections with respect to three orthogonal planes. This result provides a partial solution to a Fraser and Li conjecture. Furthermore, in [14], Peter McGrath also studies the first Steklov eigenvalue of a family of free boundary minimal surfaces on the unit ball having more general symmetries.