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Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones
- 1.0566027 - ÚJF 2023 RIV DE eng J - Journal Article
Khalile, M. - Lotoreichik, Vladimir
Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones.
Journal of Spectral Theory. Roč. 12, č. 2 (2022), s. 683-706. ISSN 1664-039X. E-ISSN 1664-0403
R&D Projects: GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : Robin Laplacian * 2-manifold * unbounded conical domain * lowest eigenvalue * spectral isoperimetric inequality * parallel coordinates
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Open access
https://doi.org/10.4171/JST/416
We consider the problem of geometric optimization of the lowest eigenvalue for the Laplacian on a compact, simply-connected two-dimensional manifold with boundary subject to an attractive Robin boundary condition. We prove that in the sub-class of manifolds with the Gauss curvature bounded from above by a constant K-o >= 0 and under the constraint of fixed perimeter, the geodesic disk of constant curvature K-o maximizes the lowest Robin eigenvalue. In the same geometric setting, it is proved that the spectral isoperimetric inequality holds for the lowest eigenvalue of the Dirichlet-to-Neumann operator. Finally, we adapt our methods to Robin Laplacians acting on unbounded three-dimensional cones to show that, under a constraint of fixed perimeter of the cross-section, the lowest Robin eigenvalue is maximized by the circular cone.
Permanent Link: https://hdl.handle.net/11104/0337466
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