Curvature estimates for gradient expanding Ricci solitons
Bull. Korean Math. Soc. 2021 Vol. 58, No. 3, 537-557
https://doi.org/10.4134/BKMS.b190805
Published online May 10, 2021
Printed May 31, 2021
Liangdi Zhang
Yanqi Lake Beijing Institute of Mathematical Sciences and Applications
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 : Curvature estimate, gradient expanding Ricci soliton, nonnegative Ricci curvature
MSC numbers : Primary 53C21, 53C25
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