Pure and Applied Mathematics Quarterly

Volume 19 (2023)

Number 6

Special Issue in honor of Professor Blaine Lawson’s 80th birthday

Guest Editors: Shiu-Yuen Cheng, Paulo Lima-Filho, and Stephen Shing-Toung Yau

Curvature in the balance: the Weyl functional and scalar curvature of $4$-manifolds

Pages: 2737 – 2763

DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n6.a5

Author

Claude LeBrun (Department of Mathematics, Stony Brook University, Stony Brook, New York, U.S.A.)

Abstract

The infimum of the Weyl functional is shown to be surprisingly small on many compact $4$-manifolds that admit positive-scalar-curvature metrics. Results are also proved that systematically compare the scalar and self-dual Weyl curvatures of certain almost-Kähler $4$-manifolds.

Keywords

four-manifold, Weyl functional, scalar curvature

2010 Mathematics Subject Classification

Primary 53C20. Secondary 57R55.

Received 2 March 2022

Accepted 4 April 2022

Published 30 January 2024