Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2401.13862 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917574365675520 |
|---|---|
| author | Kim, Hanna N. |
| author_facet | Kim, Hanna N. |
| contents | In this paper, we prove an upper bound on the second non-zero Laplacian eigenvalue on $n$-dimensional real projective space. The sharp result for 2-dimensions was shown by Nadirashvili and Penskoi and later by Karpukhin when the metric degenerates to that of the disjoint union of a round projective space and a sphere. That conjecture is open in higher dimensions, but this paper proves it up to a constant factor that tends to 1 as the dimension tends to infinity. Also, we introduce a topological argument that deals with the orthogonality conditions in a single step proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13862 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Second Laplacian eigenvalue on real projective space Kim, Hanna N. Spectral Theory In this paper, we prove an upper bound on the second non-zero Laplacian eigenvalue on $n$-dimensional real projective space. The sharp result for 2-dimensions was shown by Nadirashvili and Penskoi and later by Karpukhin when the metric degenerates to that of the disjoint union of a round projective space and a sphere. That conjecture is open in higher dimensions, but this paper proves it up to a constant factor that tends to 1 as the dimension tends to infinity. Also, we introduce a topological argument that deals with the orthogonality conditions in a single step proof. |
| title | Second Laplacian eigenvalue on real projective space |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2401.13862 |