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arXiv · 1812.04760

$\ell^2$ Decoupling in $\mathbb R^2$ for curves with Vanishing Curvature

Chandan Biswas·Maxim Gilula·Linhan Li·Jeremy Schwend·Yakun Xi
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Abstract

We expand the class of curves $(\varphi_1(t),\varphi_2(t)),\ t\in[0,1]$ for which the $\ell^2$ decoupling conjecture holds for $2\leq p\leq 6$. Our class of curves includes all real-analytic regular curves with isolated points of vanishing curvature and all curves of the form $(t,t^{1+\nu})$ for $\nu\in (0,\infty)$.

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Chandan Biswas, Maxim Gilula, Linhan Li, Jeremy Schwend, Yakun Xi. 2018-12-12. $\ell^2$ Decoupling in $\mathbb R^2$ for curves with Vanishing Curvature. https://arxiv.org/abs/1812.04760

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