Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2021; 58(3): 537-557

Online first article May 10, 2021      Printed May 31, 2021

https://doi.org/10.4134/BKMS.b190805

Copyright © The Korean Mathematical Society.

Curvature estimates for gradient expanding Ricci solitons

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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