Local solvability of degenerate Monge-Ampère equations and applications to geometry
| dc.contributor.author | Khuri, Marcus | |
| dc.date.accessioned | 2021-08-06T18:38:29Z | |
| dc.date.available | 2021-08-06T18:38:29Z | |
| dc.date.issued | 2007-05-09 | |
| dc.description.abstract | We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampère type. These are: the problem of locally prescribed Gaussian curvature for surfaces in ℝ3, and the local isometric embedding problem for two-dimensional Riemannian manifolds. We prove a general local existence result for a large class of degenerate Monge-Ampère equations in the plane, and obtain as corollaries the existence of regular solutions to both problems, in the case that the Gaussian curvature vanishes and possesses a nonvanishing Hessian matrix at a critical point. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 37 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Khuri, M. A. (2007). Local solvability of degenerate Monge-Ampère equations and applications to geometry. <i>Electronic Journal of Differential Equations, 2007</i>(65), pp. 1-37. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14227 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Local solvability | |
| dc.subject | Monge-Ampère equations | |
| dc.subject | Isometric embeddings | |
| dc.title | Local solvability of degenerate Monge-Ampère equations and applications to geometry | |
| dc.type | Article |