全球化的地方紧密的地方团体

局部紧压缩局部群

Locally Compact Contractive Local Groups

研究了局部紧压缩局部群，即具有压缩伪自同构的局部紧局部群。我们证明了，如果这样的对象是局部连通的，那么它是局部同构的李群。我们还证明了一个相关的结构定理，局部紧压缩局部群不一定是局部连通的。这些结果是局部紧压缩群定理的局部类似。

Locally conformally symplectic structures on compact non-Kähler complex surfaces

We prove that every compact complex surface with odd first Betti number admits a locally conformally symplectic $2$-form which tames the underlying almost complex structure.

On locally homogeneous pseudo-Riemannian compact einstein manifolds

We ask a general question: what are locally homogeneous compact pseudo-Riemannian Einstein manifolds? We show that any standard compact Clifford-Klein form of a simple non-compact Lie group admits at least one Einstein metric. We conjecture that these are basically the only possible locally homogeneous Einstein pseudo-Riemannian compact manifolds using T. Kobayashi's conjecture as a guiding principle.

A compactness theorem for locally homogeneous spaces

We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature $|\operatorname{sec}|\leq 1$. Moreover, we show that the set of geometric models is compact in the pointed $\mathcal{C}^{1,α}$-topology.

具有局部乘积结构的紧致黎曼自旋流形上Dirac特征值的下界

Lower bounds of the Dirac eigenvalues on compact Riemannian spin manifolds with locally product structure

研究了几乎积黎曼结构和几乎厄米特结构之间的一些相似性。受相似性的启发，我们证明了狄拉克算子在具有局部乘积结构的紧致黎曼自旋流形上的下特征值估计。我们还提供了一些例子（极限流形）的极限情况下的估计。

A characterization of compact locally conformally hyperkähler manifolds

We give an equivalent definition of compact locally conformally hyperkähler manifolds in terms of the existence of a nondegenerate complex two-form with natural properties. This is a conformal analogue of Beauville's theorem stating that a compact Kähler manifold admitting a holomorphic symplectic form is hyperkähler.