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- W4387267252 abstract "Let A be an annular end of a complete minimal surface S in Rm and let V be a k-dimension projective subvariety of Pn(C)(n=m−1). Let g be the generalized Gauss map of S into V⊂Pn(C). In this paper, we establish a modified defect relation of g on the annular end A for q hypersurfaces {Qi}i=1q of Pn(C) in N-subgeneral position with respect to V. Our result implies that the image g(A) cannot omit all q hypersurfaces Q1,…,Qq if g is nondegenerate over Id(V) and q>(2N−k+1)(M+1)(M+2d)2d(k+1), where M=HV(d)−1 and d is the least of common multiple of degQ1,…,degQq. As our best knowledge, it is the first time the value distribution of the Gauss map on an annular end of a minimal surfaces with hypersurface targets is studied, in particular the product into sum inequality for holomorphic curves on Riemann surfaces with hypersurfaces targets is presented. This our result has been used to study the unicity of the gauss maps in the recent work of C. Lu and X. Chen." @default.
- W4387267252 created "2023-10-03" @default.
- W4387267252 creator A5025520101 @default.
- W4387267252 date "2024-03-01" @default.
- W4387267252 modified "2023-10-18" @default.
- W4387267252 title "Modified defect relation of Gauss maps on annular ends of minimal surfaces for hypersurfaces of projective varieties in subgeneral position" @default.
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- W4387267252 doi "https://doi.org/10.1016/j.jmaa.2023.127806" @default.
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