Existence of the $(\alpha,\beta)$-Ricci-Yamabe flow on closed manifolds

Liangdi Zhang

Existence of the $(\alpha,\beta)$-Ricci-Yamabe flow on closed manifolds

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arxiv 2302.03199 v1 pith:CMQQ4ABP submitted 2023-02-07 math.DG math.AP

Liangdi Zhang This is my paper · ORCID

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abstract

On a smooth closed Riemannian manifold, we show short time existence of smooth solutions to the $(\alpha,\beta)$-Ricci-Yamabe flow, which is a natural generalization of the Ricci flow and the Yamabe flow. We also establish some long time existence theorems for the closed $(\alpha,\beta)$-Ricci-Yamabe flow by estimating its curvatures.

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