Harmonic functions with highly intersecting zero sets

2024/10/04 by Stojisavljević, Vukašin · 1 citation
#31B05 (Primary) #32Axx (Secondary) #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.03975

Abstract

We show that the number of isolated zeros of a harmonic map h:ℝ²→ ℝ² 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.

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