Mathematische Zeitschrift

, Volume 288, Issue 1–2, pp 311–331 | Cite as

The centro-affine invariant geometric heat flow

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Abstract

In this paper, a centro-affine invariant curve evolution process is pre-sented, and the centro-affine geometric heat flow is introduced. It is shown that the original symmetric solution of the flow shrinks to a point in finite time and converges smoothly to an ellipse after suitable normalization.

Keywords

Centro-affine geometry Geometric heat flow Long time behavior 

Mathematics Subject Classification

53C44 35L70 35L45 

Notes

Acknowledgements

The work of Wo is supported by NSF-China Grant-11201249 and Zhejiang Provincial NSF of China Grant-LY16A010002. The work of Wang is supported by NSF-China Grant-11101078, the Postdoctoral Science Foundation of China Grant-2016T90399 and Fundamental Research Funds for the Central Universities Grant-2242015R30012. The work of Qu is supported by NSF-China Grant-11631007, Grant-11471174 and Grant-11371209.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsNingbo UniversityNingboPeople’s Republic of China
  2. 2.Department of MathematicsSoutheast UniversityNanjingPeople’s Republic of China
  3. 3.Center for Nonlinear StudiesNingbo UniversityNingboPeople’s Republic of China

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