Index characterization for free boundary minimal surfaces
By Hung Tran. 2016
57 citations recorded by the source corpus.
In this paper, we compute the Morse index for a free boundary minimal submanifold from data of two simpler problems. The first one is the corresponding problem with fixed boundary condition; and the second is associated with the Dirichlet-to-Neumann map for Jacobi fields. As an application, we show that the Morse index of a free boundary minimal annulus is equal to 4 if and only if it is the critical catenoid.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1f63db391d3cd535dfe06af7d5675ac72d7263ea
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Free boundary minimal surfaces in the unit ball : recent advances and open questions (2019, methodology): “ing question: Open Question 6. Is the critical catenoid the only (up to rigid motions) immersed free boundary minimal surface in B3 with Morse index 4? Only partial results have been obtained by Tran [90] and Devyver [17]. They showed that the answer is yes if we assume additionally that the free bo”
- Free boundary minimal surfaces of unbounded genus (2016, methodology): “On the other hand, if one considers more general deformations, then its Morse index has recently been computed to be 4 ([SZ], [T], [D]).”
- Compactness analysis for free boundary minimal hypersurfaces (2017, background): “Secondly, one has witnessed a few interesting classification results towards conjectural characterisations of the critical catenoid among free boundary minimal hypersurfaces in the Euclidean unit ball [5,12,28,36,38].”