On the Morse Index with Constraints I: An Abstract Formulation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866911390476795904 |
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| author | Tran, Hung Zhou, Detang |
| author_facet | Tran, Hung Zhou, Detang |
| contents | In this sequence, we first prove an abstract Morse index theorem in a Hilbert space modeling a variational problem with constraints. Then, our abstract formulation is applied to study several optimization setups including closed CMC hypersurfaces, capillary surfaces in a ball, and critical points of type-II partitioning. In this paper, we study the index and nullity of a symmetric bounded bilinear form in a Hilbert space. The main results determine precisely how these notions change when restricting to a subspace of a finite codimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_05952 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the Morse Index with Constraints I: An Abstract Formulation Tran, Hung Zhou, Detang Differential Geometry Functional Analysis Optimization and Control 53C21, 46C05, 58E05, 49K40 In this sequence, we first prove an abstract Morse index theorem in a Hilbert space modeling a variational problem with constraints. Then, our abstract formulation is applied to study several optimization setups including closed CMC hypersurfaces, capillary surfaces in a ball, and critical points of type-II partitioning. In this paper, we study the index and nullity of a symmetric bounded bilinear form in a Hilbert space. The main results determine precisely how these notions change when restricting to a subspace of a finite codimension. |
| title | On the Morse Index with Constraints I: An Abstract Formulation |
| topic | Differential Geometry Functional Analysis Optimization and Control 53C21, 46C05, 58E05, 49K40 |
| url | https://arxiv.org/abs/2010.05952 |