On complete gradient Schouten solitons

In this paper, we prove an optimal inequality between the potential function of a complete Schouten soliton and the norm of its gradient. We also prove that these metrics have bounded scalar curvature of defined sign. As an application, we prove that the potential function of a Shrinking Schouten so...

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Bibliographic Details
Published inNonlinear analysis Vol. 221; p. 112883
Main Author Borges, Valter
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.08.2022
Subjects
Gradient estimate
Schouten flow
Schouten soliton
Volume estimate
secondary
Schouten soliton
Volume estimate
Schouten flow
Gradient estimate
primary
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Summary:In this paper, we prove an optimal inequality between the potential function of a complete Schouten soliton and the norm of its gradient. We also prove that these metrics have bounded scalar curvature of defined sign. As an application, we prove that the potential function of a Shrinking Schouten soliton grows linearly and provide optimal estimates for the growth of the volume of geodesic balls.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2022.112883