In the theory of Lagrangian submanifolds of a complex space form, the Whitney spheres play a similar role as that of totally umbilical hypersurfaces in a real space form. In this talk we introduce new higher order partial differential equations satisfied by the Whitney spheres and give new characterization of them as solutions to these equations which satisfy certain pointwise or integral extrinsic curvature assumptions. This talk is based on joint works with Dr. Jiabin Yin and Dr. Liuyang Zhang.

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