Stability of Ricci flows based on Killing conditions

Peibiao Zhao; Qihui Cai

doi:10.4134/JKMS.2009.46.6.1193

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2009; 46(6): 1193-1206

Printed November 1, 2009

https://doi.org/10.4134/JKMS.2009.46.6.1193

Stability of Ricci flows based on Killing conditions

Peibiao Zhao and Qihui Cai

Nanjing University of Science and Technology and Nanjing University of Science and Technology

Abstract

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Abstract

C. Guenther studied the stability of DeTurck flows by using maximal regularity theory and center manifolds, but these arguments can not solve the stability of Ricci flows because the Ricci flow equation is not strictly parabolic. Recognizing this deficiency, the present paper considers and obtains the stability of Ricci flows, and of quasi-Ricci flows in view of some Killing conditions.

Keywords: Ricci flows, quasi-Ricci flows, DeTurck flows, Killing conditions

MSC numbers: 28A22, 53C12