Harmonic functions with highly intersecting zero sets
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929529333743616 |
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| author | Stojisavljević, Vukašin |
| author_facet | Stojisavljević, Vukašin |
| contents | We show that the number of isolated zeros of a harmonic map $h:\mathbb{R}^2\to \mathbb{R}^2$ inside the ball of radius $r$ can grow arbitrarily fast with $r$, while its maximal modulus grows in a controlled manner. This result is an analogue, in the context of harmonic maps, of the celebrated Cornalba-Shiffman counterexamples to the transcendental Bézout problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Harmonic functions with highly intersecting zero sets Stojisavljević, Vukašin Classical Analysis and ODEs Complex Variables 31B05 (Primary), 32Axx (Secondary) We show that the number of isolated zeros of a harmonic map $h:\mathbb{R}^2\to \mathbb{R}^2$ inside the ball of radius $r$ can grow arbitrarily fast with $r$, while its maximal modulus grows in a controlled manner. This result is an analogue, in the context of harmonic maps, of the celebrated Cornalba-Shiffman counterexamples to the transcendental Bézout problem. |
| title | Harmonic functions with highly intersecting zero sets |
| topic | Classical Analysis and ODEs Complex Variables 31B05 (Primary), 32Axx (Secondary) |
| url | https://arxiv.org/abs/2410.03975 |