ALE Ricci-flat 4-manifolds and harmonic forms
演讲者
Hao Yan
时间
2024年12月09日 15:30 至 17:00
地点
A3-2-301
线上
Zoom 559 700 6085
(BIMSA)
摘要
This talk focuses on the study of Asymptotically Locally Euclidean (ALE) Ricci-flat 4-manifolds, a class of Riemannian manifolds significant in geometric analysis and mathematical physics. Starting with a review of foundational concepts such as the Ricci-flat condition and weighted Sobolev norms, we will review previous research on ALE Ricci-flat 4-manifolds. In particular, we present joint work with G. Chen, which extends the results of Biquard and Hein, offering refined expansions of harmonic forms and metrics at infinity. Utilizing techniques from b-calculus, we demonstrate a Fredholm framework that enables the construction and analysis of unique solutions to related differential equations.