If the volume of a certain type of surface, defined in a higher dimensional space in terms of complex numbers, is known, then a particular kind of metric can be defined on it; the conjecture was subsequently proved to be correct.
His major contributions include several work on conjectures, such as the Calabi conjecture, positive mass conjecture and existence of black holes, Smith conjecture, Hermitian Yang-Mills connection and stable vector bundles, Frankel conjecture and Mirror conjecture, as well as new methods and concepts of gradient estimates and Harnack inequalities, uniformization of complex manifolds, harmonic maps and rigidity, minimal submanifolds, and also open problems in geometry, covering harmonic functions with controlled growth, rank rigidity of nonpositively curved manifolds, Kahler-Einstein metrics and stability of manifolds and Mirror symmetry.
His major contributions include several work on conjectures, such as Calabi conjecture, positive mass conjecture and existence of black holes, Smith conjecture, Hermitian Yang-Mills connection and stable vector bundles, Frankel conjecture and Mirror conjecture, as well as new methods and concepts of gradient estimates and Harnack inequalities, uniformization of complex manifolds, harmonic maps and rigidity, minimal submanifolds, and also open problems in geometry, covering harmonic functions with controlled growth, rank rigidity of nonpositively curved manifolds, Kahler-Einstein metrics and stability of manifolds and Mirror symmetry.