关于横截局部共形Kählerian叶理的基本Lichnerowicz上同调的注记

共形横向各向异性流形上半线性椭圆方程的一个反问题

An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds

本文研究了共形横向各向异性流形上的半线性椭圆方程反问题，通过分析高阶线性化及Gaussian准模解的相互作用，证明了利用Dirichlet-to-Neumann映射可唯一确定未知函数q，推广了已有结果。

平面波的共形商空间，以及局部齐性背景下的 Lichnerowicz 猜想

Conformal quotients of plane waves, and Lichnerowicz conjecture in a locally homogeneous setting

本文研究平面波上的共形群作用，证明存在非等距的真余紧相似作用，并在局部齐性背景下证明了洛伦兹共形 Lichnerowicz 猜想。

Conformally covariant parameterizations for relativistic initial data

We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems. This type of parameterization is certainly more natural for non constant mean curvature initial data.

半单李群的伪共形作用

Pseudo-Conformal actions of semisimple Lie groups

本文研究半单李群在伪黎曼流形上的共形作用，证明此类流形在特定条件下为共形平坦。

On harmonic symmetries for locally conformally Kähler manifolds

In this article, we study harmonic symmetries on the compact locally conformally Kähler manifold $M$ of $dim_{\mathbb{C}}=n$. The space of harmonic symmetries is a subspace of harmonic differential forms which defined by the kernel of a certain Laplacian-type operator $\square$. We observe that the spaces $\ker(\square)\capΩ^{l}=\{0\}$ for any $|l-n|\geq2$ and $\kerΔ_{\bar{\partial}}\cap P^{k,n-1-k}\cap\ker(i_{θ^{\sharp}})\cong\ker(\square^{k,n-1-k})$, $\kerΔ_{\bar{\partial}}\cap P^{k,n-k}\cong\ker(\square^{k,n-k})$. Furthermore, suppose that $M$ is a Vaisman manifold, we prove that (i) $α$ is…

On the Lee classes of locally conformally symplectic complex surfaces

We prove that the deRham cohomology classes of Lee forms of locally conformally symplectic structures taming the complex structure of a compact complex surface $S$ with first Betti number equal to $1$ is either a non-empty open subset of $H^1_{dR}(S, \mathbb R)$, or a single point. In the latter case, we show that $S$ must be biholomorphic to a blow-up of an Inoue-Bombieri surface. Similarly, the deRham cohomology classes of Lee forms of locally conformally Kähler structures of a compact complex surface $S$ with first Betti number equal to $1$ is either a non-empty open subset of $H^1_{dR}(S, …