Nested nodal loops of biharmonic functions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917508414439424 |
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| author | Gómez-Serrano, Javier Koirala, Robert Logunov, Alexander |
| author_facet | Gómez-Serrano, Javier Koirala, Robert Logunov, Alexander |
| contents | Given any \(n\in\mathbb{N}\), we construct a real-valued biharmonic polynomial on \(\mathbb{R}^2\) whose zero set contains a nest of \(n\) smooth, disjoint topological loops, meaning that the \(k\)-th loop lies inside the domain bounded by the \((k+1)\)-st loop for \(k=1,\ldots,n-1\). The case \(n=2\), i.e., the existence of two nested loops, is related to the failure of the Boggio-Hadamard conjecture from the early 1900s. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18699 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nested nodal loops of biharmonic functions Gómez-Serrano, Javier Koirala, Robert Logunov, Alexander Analysis of PDEs 35B05, 31A30, 35J30, 35C11, 14P25 Given any \(n\in\mathbb{N}\), we construct a real-valued biharmonic polynomial on \(\mathbb{R}^2\) whose zero set contains a nest of \(n\) smooth, disjoint topological loops, meaning that the \(k\)-th loop lies inside the domain bounded by the \((k+1)\)-st loop for \(k=1,\ldots,n-1\). The case \(n=2\), i.e., the existence of two nested loops, is related to the failure of the Boggio-Hadamard conjecture from the early 1900s. |
| title | Nested nodal loops of biharmonic functions |
| topic | Analysis of PDEs 35B05, 31A30, 35J30, 35C11, 14P25 |
| url | https://arxiv.org/abs/2605.18699 |