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

  • Kyeongsu Choi EMAIL logo , Panagiota Daskalopoulos , Lami Kim and Ki-Ahm Lee

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.

Award Identifier / Grant number: DMS-1600658

Award Identifier / Grant number: DMS-1266172

Award Identifier / Grant number: 2014R1A2A2A01004618

Funding statement: P. Daskalopoulos and K. Choi have been partially supported by NSF grant DMS-1600658. In addition, P. Daskalopoulos has been partially supported by NSF grant DMS-1266172. Ki-Ahm Lee was supported by the National Research Foundation of Korea (NRF) grant 2014R1A2A2A01004618 funded by the Korea government (MSIP). Ki-Ahm Lee also holds a joint appointment with the Research Institute of Mathematics of Seoul National University.

Acknowledgements

The authors are indebted to Pengfei Guan for many fruitful discussions.

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Received: 2016-08-29
Revised: 2017-04-17
Published Online: 2017-10-06
Published in Print: 2019-12-01

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