Disc stackings and their Morse index
We construct free boundary minimal disc stackings, with any number of strata, in the three-dimensional Euclidean unit ball, and prove uniform, linear lower and upper bounds on the Morse index of all such surfaces. Among other things, our work implies for any positive integer k the existence of k-tup...
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| Language: | English |
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De Gruyter
2025-05-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2023-0177 |
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| author | Carlotto Alessandro Schulz Mario B. Wiygul David |
| author_facet | Carlotto Alessandro Schulz Mario B. Wiygul David |
| author_sort | Carlotto Alessandro |
| collection | DOAJ |
| description | We construct free boundary minimal disc stackings, with any number of strata, in the three-dimensional Euclidean unit ball, and prove uniform, linear lower and upper bounds on the Morse index of all such surfaces. Among other things, our work implies for any positive integer k the existence of k-tuples of distinct, pairwise non-congruent, embedded free boundary minimal surfaces all having the same topological type. In addition, since we prove that the equivariant Morse index of any such free boundary minimal stacking, with respect to its maximal symmetry group, is bounded from below by (the integer part of) half the number of layers, it follows that any possible realization of such surfaces via an equivariant min-max method would need to employ sweepouts with an arbitrarily large number of parameters. This also shows that it is only for N = 2 and N = 3 layers that free boundary minimal disc stackings can be obtained by means of one-dimensional mountain pass schemes. |
| format | Article |
| id | doaj-art-f84ae3bf3f1e48a3be4a4d9da46a147d |
| institution | Matheson Library |
| issn | 2169-0375 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj-art-f84ae3bf3f1e48a3be4a4d9da46a147d2025-07-28T06:08:16ZengDe GruyterAdvanced Nonlinear Studies2169-03752025-05-0125375680610.1515/ans-2023-0177Disc stackings and their Morse indexCarlotto Alessandro0Schulz Mario B.1Wiygul David2Dipartimento di Matematica, Università di Trento, via Sommarive 14, 38123, Povo di Trento, ItalyDipartimento di Matematica, Università di Trento, via Sommarive 14, 38123, Povo di Trento, ItalyDipartimento di Matematica, Università di Trento, via Sommarive 14, 38123, Povo di Trento, ItalyWe construct free boundary minimal disc stackings, with any number of strata, in the three-dimensional Euclidean unit ball, and prove uniform, linear lower and upper bounds on the Morse index of all such surfaces. Among other things, our work implies for any positive integer k the existence of k-tuples of distinct, pairwise non-congruent, embedded free boundary minimal surfaces all having the same topological type. In addition, since we prove that the equivariant Morse index of any such free boundary minimal stacking, with respect to its maximal symmetry group, is bounded from below by (the integer part of) half the number of layers, it follows that any possible realization of such surfaces via an equivariant min-max method would need to employ sweepouts with an arbitrarily large number of parameters. This also shows that it is only for N = 2 and N = 3 layers that free boundary minimal disc stackings can be obtained by means of one-dimensional mountain pass schemes.https://doi.org/10.1515/ans-2023-0177minimal surfacesfree boundary problemsmorse index53a1049q0558e12 |
| spellingShingle | Carlotto Alessandro Schulz Mario B. Wiygul David Disc stackings and their Morse index Advanced Nonlinear Studies minimal surfaces free boundary problems morse index 53a10 49q05 58e12 |
| title | Disc stackings and their Morse index |
| title_full | Disc stackings and their Morse index |
| title_fullStr | Disc stackings and their Morse index |
| title_full_unstemmed | Disc stackings and their Morse index |
| title_short | Disc stackings and their Morse index |
| title_sort | disc stackings and their morse index |
| topic | minimal surfaces free boundary problems morse index 53a10 49q05 58e12 |
| url | https://doi.org/10.1515/ans-2023-0177 |
| work_keys_str_mv | AT carlottoalessandro discstackingsandtheirmorseindex AT schulzmariob discstackingsandtheirmorseindex AT wiyguldavid discstackingsandtheirmorseindex |