Radial symmetric solution of complex Hessian equation in the unit ball

Abstract

In this note, by using fixed point theorems, we show the existence of a radial symmetric solutions for certain k-complex Hessian equation in the unit ball.

Keywords:

• complex Hessian equation
• k-subharmonic function

AMS Subject Classifications::

• 32C20
• 32U05
• 32U35
• 32U40

Acknowledgements

This note was partly written during Nguyen Thac Dung's visit to IMS, National University of Singapore. He wants to thank Prof. Louis Chen for the kind invitation. He also expresses his gratitude to NSC, Taiwan, for supporting his PhD program at National Tsinghua University, Taiwan. Nguyen Quang Dieu is supported by the NAFOSTED project 101.01-2011.13.