The first Dirichlet-Laplacian eigenvalue on polygonal domains
| dc.contributor.author | Wang, Zhichun | |
| dc.contributor.examiningcommittee | Slevinsky, Mikael (Mathematics) | |
| dc.contributor.examiningcommittee | Smailey, Mohammad (Univ. of Northern BC) | |
| dc.contributor.supervisor | Cowan, Craig | |
| dc.contributor.supervisor | Lui, Shaun | |
| dc.date.accessioned | 2023-08-10T21:11:51Z | |
| dc.date.available | 2023-08-10T21:11:51Z | |
| dc.date.issued | 2023-08-03 | |
| dc.date.submitted | 2023-08-04T01:38:58Z | en_US |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | |
| dc.description.abstract | The well-known Faber-Krahn isoperimetric inequality states that among all domains with a given volume, the ball is the minimizer of the first Dirichlet-Laplacian eigenvalue. Therefore, it's natural to make the conjecture that among all polygonal domains with a given area and a given number of sides, the regular polygon minimizes the first eigenvalue. Pólya gave a proof for triangles and quadrilaterals using the technique of Steiner symmetrization, but for polygons with more than 4 sides, this remains an open problem. A review of Pólya's classical proof and of a numerical evaluation by Bogosel and Bucur is given. Furthermore, other approaches related to the eigenvalue optimization problem, including techniques from rearrangement theory, Cheeger theory, and curvature flow theory, are explored. | |
| dc.description.note | October 2023 | |
| dc.identifier.uri | http://hdl.handle.net/1993/37454 | |
| dc.language.iso | eng | |
| dc.rights | open access | en_US |
| dc.subject | First Dirichlet-Laplacian eigenvalue | |
| dc.subject | Optimization on polygons | |
| dc.subject | Rearrangement inequalities | |
| dc.subject | Cheeger constant | |
| dc.subject | Curvature flow | |
| dc.title | The first Dirichlet-Laplacian eigenvalue on polygonal domains | |
| dc.type | master thesis | en_US |
| local.subject.manitoba | no |