Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CURVATURE ESTIMATES FOR GRADIENT EXPANDING RICCI SOLITONS

  • Zhang, Liangdi (Center of Mathematical Sciences Zhejiang University and Yanqi Lake Beijing Institute of Mathematical Sciences and Applications)
  • Received : 2019.08.30
  • Accepted : 2020.12.09
  • Published : 2021.05.31
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Abstract

In this paper, we investigate the curvature behavior of complete noncompact gradient expanding Ricci solitons with nonnegative Ricci curvature. For such a soliton in dimension four, it is shown that the Riemann curvature tensor and its covariant derivatives are bounded. Moreover, the Ricci curvature is controlled by the scalar curvature. In higher dimensions, we prove that the Riemann curvature tensor grows at most polynomially in the distance function.

Keywords

Acknowledgement

The author would like to thank Professor Kefeng Liu for his encouragement and guidance.

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