dc.contributor.advisor | Wei, Shihshu Walter | |
dc.contributor.author | Qu, Hong | |
dc.date.accessioned | 2014-12-12T17:41:54Z | |
dc.date.available | 2014-12-12T17:41:54Z | |
dc.date.issued | 2014-12 | |
dc.identifier.uri | https://hdl.handle.net/11244/13880 | |
dc.description.abstract | From a geometric point of view, we use coordinates as the main tool to define the holomorphic gradient, the antiholomorphic gradient, and the complex gradient of a complex-valued function on Kahler manifolds. Then we define the holomorphic Laplacian, the antiholomorphic Laplacian, and the complex Laplacian of a real-valued function. For the first time, we introduce the holomorphic p-Laplacian, the antiholomorphic p-Laplacian, and the complex p-Laplacian, and we find the relationship among them. We also find a relationship between the complex p-Laplacian and the usual Riemannian p-Laplacian. Finally, based on this relationship, we make global integral estimates on complete noncompact Kahler manifolds as an application of the complex p-Laplacian, the holomorphic p-Laplacian, and the antiholomorphic p-Laplacian. | en_US |
dc.language | en_US | en_US |
dc.subject | Mathematics. | en_US |
dc.subject | Holomorphic Gradient, Antiholomorphic Gradient, Complex Gradient. | en_US |
dc.subject | Holomorphic Laplacian, Antiholomorphic Laplacian, Complex Laplacian. | en_US |
dc.subject | Holomorphic p-Laplacian, Antiholomorphic p-Laplacian, Complex p-Laplacian. | en_US |
dc.subject | Kahler Manifold. | en_US |
dc.title | COMPLEX P-LAPLACIAN ON KAHLER MANIFOLDS AND ITS APPLICATIONS | en_US |
dc.contributor.committeeMember | Dai, Xinyu | |
dc.contributor.committeeMember | Albert, John | |
dc.contributor.committeeMember | Lee, Kyung-Bai | |
dc.contributor.committeeMember | Roche, Alan | |
dc.date.manuscript | 2014-12 | |
dc.thesis.degree | Ph.D. | en_US |
ou.group | College of Arts and Sciences::Department of Mathematics | en_US |
shareok.nativefileaccess | restricted | en_US |