Constant rank theorem in complex variables Qun Li 3553plurisubharmonicconstant rankcomplex Hessian equations We establish a constant rank theorem for elementary symmetric functions in terms of complex Hessian matrix in complex domains and complex manifolds. We also give some application and discussion on it. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3574 10.1512/iumj.2009.58.3574 en Indiana Univ. Math. J. 58 (2009) 1235 - 1256 state-of-the-art mathematics http://iumj.org/access/