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Jaigyoung Choe's main interest is in differential geometry. He is mainly working on geometric analysis, especially on minimal surfaces, constant mean curvature surfaces, harmonic maps, isoperimetric inequality and stability of minimal surfaces, eigenvalues of the Laplacian, capillary surfaces, construction of higher dimensional minimal submanifolds, geometric measure theory, and noncommutative minimal surfaces. He has proved the sharp isoperimetric inequality for minimal surfaces in various ambient Riemannian manifolds. Recently he constructed new minimal submanifolds in space forms and also proved that Yau's conjecture is true for some minimal surfaces in S^3 showing that the first eigenvalue of the Laplacian on Lawson's and Karcher-Pinkall-Sterling's minimal surfaces equals two.