Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Minimal immersions of punctured compact Riemann surfaces in $\textbf {R}^ 3$
HTML articles powered by AMS MathViewer

by Kichoon Yang PDF
Proc. Amer. Math. Soc. 113 (1991), 809-816 Request permission

Abstract:

We prove that a hyperelliptic Riemann surface of genus $g$ can be completely conformally and minimally immersed in ${R^3}$ with finite total curvature with at most $3g + 2$ punctures; an arbitrary compact Riemann surface of genus $g$ can be so immersed with at most $4g$ punctures. Moreover, we show that there is at least a one-parameter family of nonisometric such immersions for a given punctured compact Riemann surface. Our results improve earlier results of Gackstatter-Kunert and the author.
References
Similar Articles
Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 809-816
  • MSC: Primary 53A10; Secondary 30F10, 49Q10, 53C42
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1069297-6
  • MathSciNet review: 1069297