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On a complex Hessian
flow
Weimin Sheng and Jiaxiang Wang |
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Vol. 300 (2019), No. 1, 159–177
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Abstract |
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We consider a gradient flow generated by a complex Hessian functional which is defined on compact Kähler manifolds. By setting up the a priori estimates of the admissible solutions, we prove the long-time existence of the solution to the flow and its convergence. Thus we show the functional admits a local minimal point in the space of admissible functions. As its application, we show the solvability of a class of complex Hessian equations. |
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Keywords
fully nonlinear flow, complex Hessian equation
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Mathematical Subject Classification 2010
Primary: 35K55, 53C44, 53C55
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Milestones
Received: 6 January 2018
Revised: 14 August 2018
Accepted: 22 August 2018
Published: 20 July 2019
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Authors |
| Weimin Sheng | |
| School of Mathematical
Sciences Zhejiang University Hangzhou China |
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| Jiaxiang Wang | |
| School of Mathematical
Sciences Zhejiang University Hangzhou China |
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