In this paper,we study the value distribution properties of the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(m),which is the case where the generalized Gauss mapΦis ramified over a famil...In this paper,we study the value distribution properties of the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(m),which is the case where the generalized Gauss mapΦis ramified over a family of hypersurfaces{Q_(j)}_(j=1)^(q)in P^(m-1)(C)located in the N-subgeneral position.In addition,we investigate the Gauss curvature estimate for the K-quasiconformal harmonic surfaces immersed in R^(3)whose Gauss maps are ramified over a family of hypersurfaces located in the N-subgeneral position.展开更多
Let M be an oriented surface and G(2,k) be the Grassmannian.Smooth maps t1 M→G2（2，k) are studied to determine whether or not they are Gauss maps.Some new results have been obtained and some known results reproved.
基金supported by the NFSC(11971182,12271189)the NFS of Fujian Province of China(2019J01066,2021J01304)。
文摘In this paper,we study the value distribution properties of the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(m),which is the case where the generalized Gauss mapΦis ramified over a family of hypersurfaces{Q_(j)}_(j=1)^(q)in P^(m-1)(C)located in the N-subgeneral position.In addition,we investigate the Gauss curvature estimate for the K-quasiconformal harmonic surfaces immersed in R^(3)whose Gauss maps are ramified over a family of hypersurfaces located in the N-subgeneral position.
文摘Let M be an oriented surface and G(2,k) be the Grassmannian.Smooth maps t1 M→G2（2，k) are studied to determine whether or not they are Gauss maps.Some new results have been obtained and some known results reproved.
