In this paper, we study the value distribution properties of the generalized Gauss maps of weakly complete harmonic surfaces immersed in $\mathbb{R}^{m}$, which is the case where the generalized Gauss map $\Phi$ is ramified over a family of hypersurfaces $\{Q_{j}\}_{j=1}^{q}$ in $\mathbb{P}^{m-1}(\mathbb{C})$ located in the $N$-subgeneral position. In addition, we investigate the Gauss curvature estimate for the $K$-quasiconformal harmonic surfaces immersed in $\mathbb{R}^{3}$ whose Gauss maps are ramified over a family of hypersurfaces located in the $N$-subgeneral position.
Canhui LU
,
Xingdi CHEN
. VALUE DISTRIBUTION PROPERTIES FOR GAUSS MAPS OF IMMERSED HARMONIC SURFACES RAMIFIED OVER HYPERSURFACES[J]. Acta mathematica scientia, Series B, 2024
, 44(6)
: 2341
-2360
.
DOI: 10.1007/s10473-024-0616-y
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