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arXiv · 1309.2373

On sharp local turns of planar polynomials

Ruixiang Zhang
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Abstract

We show that for a real polynomial of degree $n$ in two variables $x$ and $y$, any local "sharp turn" must have its "size" $\gtrsim e^{-Cn^{2}}$. We also show that there is indeed an example that has a sharp turn of size $\lesssim e^{-Cn}$. This gives a quite satisfactory answer to a problem raised by Guth. The problem was inspired by applications of the polynomial method in the study of Kakeya conjecture.

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Ruixiang Zhang. 2014-03-06. On sharp local turns of planar polynomials. https://arxiv.org/abs/1309.2373

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