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Spectral estimates
for free boundary minimal surfaces via Montiel–Ros
partitioning methods
Alessandro Carlotto, Mario B. Schulz and David Wiygul |
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Vol. 18 (2025), No. 7, 1715–1768
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Abstract |
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We adapt and extend the Montiel–Ros methodology to compact manifolds with boundary, allowing for mixed (including oblique) boundary conditions and also accounting for the action of a finite group together with an additional twisting homomorphism O(1). We then apply this machinery in order to obtain quantitative lower and upper bounds on the growth rate of the Morse index of free boundary minimal surfaces with respect to the topological data (i.e., the genus and the number of boundary components) of the surfaces in question. In particular, we compute the exact values of the equivariant Morse index and nullity for two infinite families of examples, with respect to their maximal symmetry groups, and thereby derive explicit two-sided linear bounds when the equivariance constraint is lifted. |
Keywords
minimal surfaces, Morse index, equivariant spectrum
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Mathematical Subject Classification
Primary: 53A10
Secondary: 49Q05, 58C40
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Milestones
Received: 15 January 2023
Revised: 3 May 2024
Accepted: 20 July 2024
Published: 13 June 2025
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Authors |
| Alessandro Carlotto | |
| Dipartimento di Matematica Università di Trento Povo Italy |
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| Mario B. Schulz | |
| Dipartimento di Matematica Università di Trento Povo Italy |
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| David Wiygul | |
| Dipartimento di Matematica Università di Trento Povo Italy |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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