| dc.contributor.author | Deng, Jialong | |
| dc.date.accessioned | 2025-12-17T09:41:33Z | |
| dc.date.available | 2025-12-17T09:41:33Z | |
| dc.date.issued | 2025-12 | |
| dc.identifier.uri | https://publications.mfo.de/handle/mfo/4357 | |
| dc.description | The author acknowledges support from the Oberwolfach Leibniz Fellows programme (MFO), the YMSC Overseas Shuimu Scholarship, the Simons Center for Geometry and Physics, and ICMS Edinburgh (workshops on Geometric Measure Theory on Metric Spaces with Applications to Physics and Geometry and Geometric Moduli Spaces, respectively). I thank Gerhard Huisken for discussions on the Ricci flow. This work originates from a broader project initiated during my postdoctoral stay at the Yau Center. During that time, this work was also supported by NSFC 12401063 and partially by NSFC 12271284. I am deeply grateful to Shing-Tung Yau and Akito Futaki for their trust and support, which allowed me to pursue independent research. | en_US |
| dc.description.abstract | We prove that every locally conformally flat metric on a closed, oriented hyperbolic $4$-manifold with scalar curvature bounded below by $-12$ satisfies Schoen’s conjecture. We also classify all closed Riemannian $4$-manifolds of positive scalar curvature that arise as total spaces of fibre bundles. For a closed locally conformally flat manifold $(M^4,g)$ with scalar-flat and $\pi_2(M^4) \neq 0$, we show that the universal Riemannian cover $(\widetilde{M},\tilde{g})$ is homothetic to the standard product $\mathbb{H}^2 \times \mathbb{S}^2$. This affirmatively answers a question of N. H. Noronha. | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Mathematisches Forschungsinstitut Oberwolfach | en_US |
| dc.relation.ispartofseries | Oberwolfach Preprints;2025-14 | |
| dc.title | Scalar Curvature in Dimension 4 | en_US |
| dc.type | Preprint | en_US |
| dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | de |
| dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | en |
| dc.identifier.doi | 10.14760/OWP-2025-14 | |
| local.scientificprogram | OWLF 2025 | |
| local.series.id | OWP-2025-14 | en_US |
| dc.identifier.ppn | 1947880713 | |
