Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1585-1597.

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Second Main Theorem for Algebraic Curves on Compact Riemann Surfaces

Lizhen Duan,Hongzhe Cao*()   

  1. Department of Mathematics, College of Science, Nanchang University, Nanchang 330031
  • Received:2020-09-25 Online:2021-12-26 Published:2021-12-02
  • Contact: Hongzhe Cao;
  • Supported by:
    the NSFC(12061041);the NSFC(12061042)


In this paper, we first establish some second main theorems for algebraic curves from a compact Riemann surface into a complex projective subvariety of the complex projective space, which is ramified over hypersurfaces in subgeneral position. Then we use it to study the ramification for the generalized Gauss map of complete regular minimal surfaces in $\mathbb{R}^{m}$ with finite total curvature.

Key words: Second main theorem, Gauss map of minimal surfaces, Algebraic curves, Hypersurfaces

CLC Number: 

  • O174.5