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The homogeneous complex Monge-Ampère equation and the infinite dimensional versions of classic symmetric spaces. (English) Zbl 0860.35031
Gelfand, I. M. (ed.) et al., The Gelfand Mathematical Seminars, 1993-1995. Papers from the seminars, held at Rutgers University, New Brunswick, New Jersey, USA and at IHES, Bures-sur-Yvette, France. Boston, MA: Birkhäuser. The Gelfand Mathematical Seminars. 225-242 (1996).
The homogeneous complex Monge-Ampère equation arises very naturally in several complex variables, in part because of its invariance under biholomorphic changes of coordinates. I describe some correspondences between its solutions, special families of mappings and submanifolds in finite-dimensional holomorphic symplectic manifolds, and curves and surfaces in certain infinite-dimensional locally symmetric spaces.
For the entire collection see [Zbl 0839.00007].

35J60 Nonlinear elliptic equations
32W20 Complex Monge-Ampère operators
32Q99 Complex manifolds