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摘要
We prove a Liouville type theorem for entire maximal m-subharmonic functions in C-n with bounded gradient. This result, coupled with a standard blow-up argument, yields a (nonexplicit) a priori gradient estimate for the complex Hessian equation on a compact Kaliler manifold. This terminates the program, initiated by Hou, Ma, and Wu, of solving the non-degenerate Hessian equation on such manifolds in full generality. We also obtain, using our previous work, continuous weak solutions in the degenerate case for the right-hand side in some LP, with a sharp bound on p.
- 出版日期2017-4
- 单位rutgers
