Year: 2026
Type: preprint
Abstract: Let $Ω\subset\mathbb{R}^2$ be a bounded domain whose boundary is a finite union of pairwise disjoint Jordan curves. We prove the planar Khavinson--Shapiro conjecture in this setting: if every polynomial on $\mathbb{R}^2$ agrees on $\partialΩ$ with a harmonic polynomial, then $\partialΩ$ is an ellipse and $Ω$ is its bounded interior.
Source: arXiv (Cornell University)
Authors: Shao, Feng, Zhan, Weicheng
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204963556