Some aspects of Ricci flow on the 4-sphere

Sun Yung Alice Chang; Eric Chen

doi:10.53733/152

Some aspects of Ricci flow on the 4-sphere

Sun Yung Alice Chang, Eric Chen

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize the standard 4-sphere. We obtain a conformal gap theorem, and for Yamabe metrics of positive scalar curvature with the L²norm of the Weyl tensor of the metric suitably small, we establish the monotonic decay of the L^pnorm for certain p > 2 of the reduced curvature tensor along the normalized Ricci flow, with the metric converging exponentially to the standard 4-sphere.

Original language	English (US)
Pages (from-to)	381-402
Number of pages	22
Journal	New Zealand Journal of Mathematics
Volume	52
DOIs	https://doi.org/10.53733/152
State	Published - 2021

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics
Geometry and Topology
Algebra and Number Theory

Keywords

Conformal invariants
Gap theorem
Ricci flow

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10.53733/152

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abstract = "In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize the standard 4-sphere. We obtain a conformal gap theorem, and for Yamabe metrics of positive scalar curvature with the L2norm of the Weyl tensor of the metric suitably small, we establish the monotonic decay of the Lpnorm for certain p > 2 of the reduced curvature tensor along the normalized Ricci flow, with the metric converging exponentially to the standard 4-sphere.",

keywords = "Conformal invariants, Gap theorem, Ricci flow",

author = "Chang, {Sun Yung Alice} and Eric Chen",

year = "2021",

doi = "10.53733/152",

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AU - Chen, Eric

PY - 2021

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AB - In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize the standard 4-sphere. We obtain a conformal gap theorem, and for Yamabe metrics of positive scalar curvature with the L2norm of the Weyl tensor of the metric suitably small, we establish the monotonic decay of the Lpnorm for certain p > 2 of the reduced curvature tensor along the normalized Ricci flow, with the metric converging exponentially to the standard 4-sphere.

KW - Conformal invariants

KW - Gap theorem

KW - Ricci flow

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JO - New Zealand Journal of Mathematics

JF - New Zealand Journal of Mathematics

ER -

Some aspects of Ricci flow on the 4-sphere

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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