# zbMATH — the first resource for mathematics

Minimal discs with free boundaries in a Lagrangian submanifold of $$\mathbb{C}^n$$. (English) Zbl 1010.58500
Summary: The question when an energy functional stationary disc $$p$$ with free boundary in a Lagrangian submanifold of $$\mathbb{C}^n$$ is holomorphic or antiholomorphic is considerd. A partial answer is given in terms of its partial indices [see J. Globevnik, Math. Z. 217, No. 2, 287-316 (1994; Zbl 0806.58044)]. It is proved that if all its partial indices are greater or equal to $$-1$$, then the stationary disc $$p$$ is holomorphic, and if all its partial indices are less or equal to 1, the disc $$p$$ is antiholomorphic (a consequence of Y.-G. Oh [Kyungpook Math. J. 35, No. 1, 39-75 (1995; Zbl 0853.32017)]).

##### MSC:
 58E12 Variational problems concerning minimal surfaces (problems in two independent variables) 32F99 Geometric convexity in several complex variables
Full Text: