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- W4386081489 abstract "Let $X:Mrightarrow{mathbb R}^3$ denote a $K$-quasiconformal harmonic surface and let $mathfrak{n}$ be the unit normal map of $M$. We define $d(p)$ as the distance from point $p$ to the boundary of $M$ and $mathcal{K}(p)$ as the Gauss curvature of $M$ at $p$. Assuming that the Gauss map (i.e., the normal $mathfrak{n}$) omits $7$ directions $mathbf{d}_1,cdots,mathbf{d}_7$ in $S^2$ with the property that any three of these directions are not contained in a plane in ${mathbb R}^3$. Then there exists a positive constant $C$ depending only on $mathbf{d}_1,cdots,mathbf{d}_7$ such that begin{equation*} |mathcal{K}(p)|leq C/d(p)^2 end{equation*} for all points $pin M$. Furthermore, a modified defect relation for the generalized Gauss map of the immersed harmonic surfaces in $mathbb{R}^n(ngeq 3)$ is verified." @default.
- W4386081489 created "2023-08-23" @default.
- W4386081489 creator A5021842480 @default.
- W4386081489 date "2023-08-21" @default.
- W4386081489 modified "2023-09-27" @default.
- W4386081489 title "An estimation of the Gauss curvature and the modified defect relation for the Gauss map of immersed harmonic surfaces in $mathbb{R}^n$" @default.
- W4386081489 doi "https://doi.org/10.48550/arxiv.2308.10507" @default.
- W4386081489 hasPublicationYear "2023" @default.
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