论文标题
$ l^2 $谐波理论，Seiberg-Witten理论和差异形式的渐近学
$L^2$ harmonic theory, Seiberg-Witten theory and asymptotics of differential forms
论文作者
论文摘要
我们呈现一对互惠同构的开放式$ 4 $ - manifolds。他们中的一个承认具有准圆柱状的Riemannian度量，标量曲率的积极性和某些$ l^2 $谐波形式的尺寸。相比之下，对于其他歧管，没有riemannian度量可以同时满足这些特性。我们的方法在紧凑型$ 4 $ -Manifolds上使用Seiberg-Witten理论，并应用$ l^2 $谐波理论对非紧凑，完整的Riemannian $ 4 $ -Manifolds。我们介绍了一个新的论点来应用轨距理论，该理论是由于发现差异范围的渐近性能而引起的。
We present a pair of open smooth $4$-manifolds that are mutually homeomorphic. One of them admits a Riemannian metric that possesses quasi-cylindricity, and positivity of scalar curvature and of dimension of certain $L^2$ harmonic forms. By contrast, for the other manifold, no Riemannian metric can simultaneously satisfy these properties. Our method uses Seiberg-Witten theory on compact $4$-manifolds and applies $L^2$ harmonic theory on non-compact, complete Riemannian $4$-manifolds. We introduce a new argument to apply Gauge theory, which arises from a discovery of an asymptotic property of the range of the differential.
