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On a Class of Complex Monge-Ampère Type Equations on Hermitian Manifolds
Sun, Wei

2013, Doctor of Philosophy, Ohio State University, Mathematics.
We study the Dirichlet problem for a class of complex Monge-Ampère equations on Hermitian manifolds with smooth boundary and data, which turns to second order fully nonlinear elliptic differential equations. Under the condition that there exists an admissible subsolution, we solve the problem by method of continuity. To apply the standard arguments, the key step is to derive a priori estimates up to second order derivatives.


Also, we are interested in the equations on closed manifolds, i.e. compact manifolds without boundary. A new relationship between χ and ω is discovered, and can help us derive sharper C2 estimates. Based on the new estimates, we can derive the C0 estimate and then C estimates on closed Hermitian manifolds.

Besides the method of continuity, parabolic flow method is also an effective way to solve second order elliptic equations. We introduce the related parabolic flows, and investigate the regularity and existence of solutions to the flows. To apply Evans-Krylov theory and Schauder estimates, we establish a priori estimates up to second order derivatives of admissible solutions. As a result, an admissible solution converges to a stationary solution, which solves the Dirichlet problem.
Bo Guan (Advisor)
Barbara Keyfitz (Committee Member)
Jeffery McNeal (Committee Member)
Victor Jin (Other)
102 p.

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Sun, W. (2013). On a Class of Complex Monge-Ampère Type Equations on Hermitian Manifolds. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Sun, Wei. "On a Class of Complex Monge-Ampère Type Equations on Hermitian Manifolds." Electronic Thesis or Dissertation. Ohio State University, 2013. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Sun, Wei "On a Class of Complex Monge-Ampère Type Equations on Hermitian Manifolds." Electronic Thesis or Dissertation. Ohio State University, 2013. https://etd.ohiolink.edu/

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