Eigenvalue lower bounds through a generalized inradius
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1.
Ludwig-Maximilians-Universität München
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2.
Munich Center for Quantum Science and Technology
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3.
California Institute of Technology
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4.
Imperial College London
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5.
Nazarbayev University
Abstract
Lieb has shown a lower bound on the smallest Dirichlet eigenvalue of the Laplace operator in terms of a generalized inradius. We derive similar bounds for Robin eigenvalues, for eigenvalues of the polyharmonic operator and the sub-Laplacian on the Heisenberg group. We propose a method based on Hardy inequalities that is different from Lieb's approach.
Copyright and License
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Funding
The authors were supported in parts by US National Science Foundation grant DMS-1954995 (R.L.F.) and the German Research Foundation grants EXC-2111-390814868 and TRR 352-Project-ID 470903074 (R.L.F.). This research is funded by Nazarbayev University under the FDCRGP 110326FD3205 (D.S.).
Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2509.18878 (arXiv)
Funding
- National Science Foundation
- DMS-1954995
- Deutsche Forschungsgemeinschaft
- EXC-2111-390814868
- Deutsche Forschungsgemeinschaft
- TRR 352-Project-ID 470903074
- Nazarbayev University
- 110326FD3205
Caltech Custom Metadata
- Caltech groups
- Division of Physics, Mathematics and Astronomy (PMA) , Mathematics Department
- Publication Status
- Published