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arXiv · 1102.2462

Smooth counterexamples to strong unique continuation for a Beltrami system in $\mathbb{C}^2$

Adam Coffman·Yifei Pan
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Abstract

We construct an example of a smooth map $\mathbb{C}\to\mathbb{C}^2$ which vanishes to infinite order at the origin, and such that the ratio of the norm of the $\bar z$ derivative to the norm of the $z$ derivative also vanishes to infinite order. This gives a counterexample to strong unique continuation for a vector valued analogue of the Beltrami equation.

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Adam Coffman, Yifei Pan. 2011-02-11. Smooth counterexamples to strong unique continuation for a Beltrami system in $\mathbb{C}^2$. https://arxiv.org/abs/1102.2462

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