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- W4366459747 abstract "In this paper we study curvature estimates for nodal sets of harmonic functions in the plane. We prove that at any point $p$, the curvature of any nodal curve of a harmonic function $u$ is upper bounded by $$ left|{kappa(u)(p)}right|leq frac{8}{nr} $$ where $u$ has only $n$ nodal curves in $B_r(p)$ across $p$. This result is sharp, for which the equality case can be characterized when $u$ is the real part of some holomorphic function related to Koebe functions. This curvature estimate was known only for $n=1$ by {U}. Kuran. Our result extends it to general case, and yields the equality case. Thus we prove that, for harmonic functions, the curvature of every nodal curve at any point $p$ is upper bounded by the distance between $p$ and other nodal curves, and the distance from $p$ to the boundary of the domain." @default.
- W4366459747 created "2023-04-22" @default.
- W4366459747 creator A5006414413 @default.
- W4366459747 date "2023-04-18" @default.
- W4366459747 modified "2023-09-25" @default.
- W4366459747 title "Curvature Estimate of Nodal Sets of Harmonic Functions in the Plane" @default.
- W4366459747 doi "https://doi.org/10.48550/arxiv.2304.09022" @default.
- W4366459747 hasPublicationYear "2023" @default.
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