New volume comparison with almost Ricci soliton
Commun. Korean Math. Soc.
Published online May 13, 2022
Shahroud azami and Sakineh Hajiaghasi
Imam Khomeini International University; Imam Khomeini International University
Abstract : In this paper, we consider a condition on the Ricci curvature involving vector fields which enabled us to achieve new results for volume comparison and Laplacian comparison. These results in special case obtained with considering volume non-collapsing condition. Also, by applying this condition we get new results of volume comparison for almost Ricci solitons.
Keywords : volume comparison, Bakry-{\'E}mery Ricci curvature
MSC numbers : 53C21, 58C25
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