A conformally invariant sphere theorem in four dimensions

By S. Chang, M. Gursky, Paul Yang. 2003

137 citations recorded by the source corpus.

0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 1 An existence result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 2 The proof of Theorem A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 3 A Weitzenbock formula for Bach–flat metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4 The proof of Theorem C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a274a758914cb31d56e2e455e47384ec91a056af

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In Applied Mathematics

1. C. B. Ndiaye
2. A. Malchiodi
3. Z. Djadli
4. Daniele Bartolucci
5. Jun-cheng Wei
6. Alessandro Carlotto
7. Yanyan Li
8. L. Martinazzi

In Astronomy and Astrophysics

1. Z. Djadli
2. A. Malchiodi
3. C. B. Ndiaye

In Geometry and Topology

1. C. B. Ndiaye
2. Z. Djadli
3. A. Malchiodi
4. L. Martinazzi

Citations in the corpus

• Existence of conformal metrics with constant Q-curvature (2004, background): “The solvability of (8), under the above hypotheses, has been useful in the study of some conformally invariant fully non-linear equations, as is shown in [13].”
• The inequality of Moser and Trudinger and applications to conformal geometry (2003, unknown): “2 (Chang, Gursky, and Yang [13]) Suppose (M 4, g) is a closed 4manifold whose conformal Laplacian is positive.”
• Morse theory and a scalar field equation on compact surfaces (2008, methodology): “We refer to the survey [16] or to [13], [29] for details and applications.”
• Constant Q-curvature metrics in arbitrary dimension (2007, background): “... by Margerin, [45] with a conformally invariant assumption, while the one of Margerin assumes pointwise pinching conditions on the Ricci tensor in terms of Wg. Finally, we also point out that the Paneitz operator, the Q-curvature and their high-dimensional analogues, see [7] , [8] appear in the s”