| Abstract: |
| We consider sets of finite perimeter $E \subset \mathbb{R}^n$ which are Ahlfors regular. On one hand, we use singular integrals to connect the Poisson kernels of $\mathbb{R}^n\setminus E$ with the unit outer normal of $E$. On the other hand, we use arguments in geometric measure theory to show that small oscillations of the unit normal implies $E$ is Reifenberg flat. Combined we get a characterization of vanishing chord-arc domains by Poisson kernels, under much weaker assumptions than previous work of Kenig-Toro. |
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