The evolution of complete non-compact graphs by powers of Gauss curvature

Kyeongsu Choi 1 , Panagiota Daskalopoulos 2 , Lami Kim 3 ,  and Ki-Ahm Lee 4
  • 1 Department of Mathematics, Columbia University, 2990 Broadway, New York, USA
  • 2 Department of Mathematics, Columbia University, 2990 Broadway, New York, USA
  • 3 Department of Mathematics, Tokyo Institute of Technology, 152-8550, Ookayama, Japan
  • 4 Department of Mathematical Sciences, Seoul National University, 151-747, Seoul, Republic of Korea
Kyeongsu Choi
  • Corresponding author
  • Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, USA
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, Panagiota Daskalopoulos, Lami Kim and Ki-Ahm Lee
  • Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, Center for Mathematical Challenges, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea
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Abstract

We prove the all-time existence of non-compact, complete, strictly convex solutions to the α-Gauss curvature flow for any positive power α.

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The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle’s Journal. In the 190 years of its existence, Crelle’s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals.

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