Area Variations under Legendrian Constraint
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916273488658432 |
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| author | Rivière, Tristan |
| author_facet | Rivière, Tristan |
| contents | In any 5 dimensional closed Sasakian manifold we prove that any minmax operation on the area among Legendrian surfaces is achieved by a continuous conformal Legendrian map from a closed riemann surface $S$ into $N^5$ equipped with an integer multiplicity bounded in $L^\infty$. Moreover this map, equipped with this multiplicity, satisfies a weak version of the Hamiltonian Minimal Equation. We conjecture that any solution to this equation is a smooth branched Legendrian immersion away from isolated Schoen-Wolfson conical singularities with non zero Maslov class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10633 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Area Variations under Legendrian Constraint Rivière, Tristan Differential Geometry Analysis of PDEs 53D12, 49Q05, 53A10, 58E12, 49Q10 In any 5 dimensional closed Sasakian manifold we prove that any minmax operation on the area among Legendrian surfaces is achieved by a continuous conformal Legendrian map from a closed riemann surface $S$ into $N^5$ equipped with an integer multiplicity bounded in $L^\infty$. Moreover this map, equipped with this multiplicity, satisfies a weak version of the Hamiltonian Minimal Equation. We conjecture that any solution to this equation is a smooth branched Legendrian immersion away from isolated Schoen-Wolfson conical singularities with non zero Maslov class. |
| title | Area Variations under Legendrian Constraint |
| topic | Differential Geometry Analysis of PDEs 53D12, 49Q05, 53A10, 58E12, 49Q10 |
| url | https://arxiv.org/abs/2306.10633 |