Quantitative Spectral Stability for an Embedded Annulus under Coupled Curve Shortening and $2$D Ricci Flows
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866909996580601856 |
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| author | Habibivostakolaei, Mohammadjavad |
| author_facet | Habibivostakolaei, Mohammadjavad |
| contents | We study the spectral stability of Dirichlet eigenvalues on an embedded annulus whose boundary evolves by curve shortening flow while the ambient surface evolves under the two dimensional Ricci flow using variational formulas, Rellich--type identities, and harmonic capacity methods, we relate eigenvalue variations to geometric deficit and modulus. We establish quantitative bounds comparing the spectrum of the evolving annulus with that of a flat cylinder of equal modulus. As a consequence, we obtain geometric stability and a spectral gap estimate controlled by the deficit functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14575 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitative Spectral Stability for an Embedded Annulus under Coupled Curve Shortening and $2$D Ricci Flows Habibivostakolaei, Mohammadjavad Differential Geometry Spectral Theory 35P15, 53C44, 58J50 We study the spectral stability of Dirichlet eigenvalues on an embedded annulus whose boundary evolves by curve shortening flow while the ambient surface evolves under the two dimensional Ricci flow using variational formulas, Rellich--type identities, and harmonic capacity methods, we relate eigenvalue variations to geometric deficit and modulus. We establish quantitative bounds comparing the spectrum of the evolving annulus with that of a flat cylinder of equal modulus. As a consequence, we obtain geometric stability and a spectral gap estimate controlled by the deficit functional. |
| title | Quantitative Spectral Stability for an Embedded Annulus under Coupled Curve Shortening and $2$D Ricci Flows |
| topic | Differential Geometry Spectral Theory 35P15, 53C44, 58J50 |
| url | https://arxiv.org/abs/2601.14575 |