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arXiv · 2410.03975

Harmonic functions with highly intersecting zero sets

Vukašin Stojisavljević
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Abstract

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 B\'{e}zout problem.

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Vukašin Stojisavljević. 2024-10-04. Harmonic functions with highly intersecting zero sets. https://arxiv.org/abs/2410.03975

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