Title:
On the Second Eigenvalue of the Laplace Operator Penalized by Curvature
On the Second Eigenvalue of the Laplace Operator Penalized by Curvature
| dc.contributor.author | Harrell, Evans M. | |
| dc.contributor.corporatename | Georgia Institute of Technology. School of Mathematics | |
| dc.date.accessioned | 2009-08-13T17:18:14Z | |
| dc.date.available | 2009-08-13T17:18:14Z | |
| dc.date.issued | 1994 | |
| dc.description | Mathematics subject classification: 58G25. | en |
| dc.description.abstract | Consider the operator - ∇^2 - q(κ), where - ∇^2 is the (positive) Laplace-Beltrami operator on a closed manifold of the topological type of the two-sphere S^2 and q is a symmetric non-negative quadratic form in the principal curvatures. Generalizing a well-known theorem of J. Hersch for the Laplace-Beltrami operator alone, it is shown in this note that the second eigenvalue λ [1] is uniquely maximized, among manifolds of fixed area, by the true sphere. | en |
| dc.identifier.uri | http://hdl.handle.net/1853/29542 | |
| dc.language.iso | en_US | en |
| dc.publisher | Georgia Institute of Technology | en |
| dc.relation.ispartofseries | CDSNS94-179 | en |
| dc.subject | Laplace-Beltrami operators | en |
| dc.subject | Curvatures | en |
| dc.subject | Eigenvalues | en |
| dc.title | On the Second Eigenvalue of the Laplace Operator Penalized by Curvature | en |
| dc.type | Text | |
| dc.type.genre | Pre-print | |
| dspace.entity.type | Publication | |
| local.contributor.author | Harrell, Evans M. | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
| relation.isAuthorOfPublication | f4970e81-552d-4cbb-afa2-d680962b0a59 | |
| relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
| relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 |