Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


Thesis.pdf (457.63 KB)

ETD Abstract Container

Abstract Header

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

Sun, Wei
http://rave.ohiolink.edu/etdc/view?acc_num=osu1366286119

Abstract Details

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.
Mathematics

Recommended Citations

Citations

  • Sun, W. (2013). On a Class of Complex Monge-Ampère Type Equations on Hermitian Manifolds [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366286119

    APA Style (7th edition)

  • Sun, Wei. On a Class of Complex Monge-Ampère Type Equations on Hermitian Manifolds. 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1366286119.

    MLA Style (8th edition)

  • Sun, Wei. "On a Class of Complex Monge-Ampère Type Equations on Hermitian Manifolds." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366286119

    Chicago Manual of Style (17th edition)

osu1366286119
847
© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.