manuscripta mathematica

, Volume 102, Issue 2, pp 177–186 | Cite as

Nonexistence of nonpositively curved surfaces¶with one embedded end

  • Hsungrow Chan


We prove certain complete nonpositively curved surfaces arising from general relativity isometrically immersible in R 3 do not exist, assuming square integrable second fundamental form. We provide an example showing the sharpness of our conditions.

Mathematics Subject Classification (1991):Primary 53C21; Secondary 53C42 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hsungrow Chan
    • 1
  1. 1.National Ping-Tung Teachers College and NCTS, Tsing Hua University, Taiwan. e-mail:

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