论文标题
高斯图的修饰缺陷关系在最小表面的环形末端，用于射线属位置的射影曲面
Modified defect relation of Gauss maps on annular ends of minimal surfaces for hypersurfaces of projective varieties in subgeneral position
论文作者
论文摘要
让$ a $是完整的最小表面$ s $ in $ \ mathbb r^m $的环状，让$ v $为$ k $ - dimension juptive juppartive jubsvariety $ \ mathbb p^n（\ mathbb c）\（n = m-1）$。令$ g $为$ s $的广义高斯地图$ v \ subset \ mathbb p^n（\ mathbb c）$。在本文中，我们建立了$ g $ $ g $的修改后的$ g $ $ a $ for $ q $ hypersurfaces $ \ {q_i \} _ {i = 1}^q $ of $ \ mathbb p^n（\ mathbb c）in $ n $ n $ n $ n $ n $ n $ v $。我们的结果意味着图像$ g（a）$不能忽略所有$ q $ hypersurfaces $ q_1，\ ldots，q_q $，如果$ g $不超过$ i_d（v）$和$ q>>> \ frac {（2n-k+1）（m+1）（m+2d）（m+2d）（m+2d）; $ d $是$°Q_1，\ ldots，°Q_Q $的最少常见倍数。据我们所知，这是首次研究高斯图在最小表面的环形末端的高表面靶标的价值分布，特别是在带有超曲面靶标的Riemann表面上的群体曲线上，产物陷入了总和不平等。我们的结果已用于研究C. lu和X. Chen [14]的最新工作中高斯图的统一性。
Let $A$ be an annular end of a complete minimal surface $S$ in $\mathbb R^m$ and let $V$ be a $k$-dimension projective subvariety of $\mathbb P^n(\mathbb C)\ (n=m-1)$. Let $g$ be the generalized Gauss map of $S$ into $V\subset\mathbb P^n(\mathbb C)$. In this paper, we establish a modified defect relation of $g$ on the annular end $A$ for $q$ hypersurfaces $\{Q_i\}_{i=1}^q$ of $\mathbb P^n(\mathbb C)$ in $N$-subgeneral position with respect to $V$. Our result implies that the image $g(A)$ cannot omit all $q$ hypersurfaces $Q_1,\ldots,Q_q$ if $g$ is nondegenerate over $I_d(V)$ and $q>\frac{(2N-k+1)(M+1)(M+2d)}{2d(k+1)}$, where $M=H_V(d)-1$ and $d$ is the least of common multiple of $°Q_1,\ldots,°Q_q$. 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 [14].
