D-log and formal flow for analytic isomorphisms of n-space

A Dolbeault Isomorphism Theorem in Infinite Dimensions

For a large class of separable Banach spaces, we prove the real analytic Dolbeault Isomorphism Theorem for open subsets.

复解析空间的orbifold修改

Orbifold modifications of complex analytic spaces

本文研究复解析空间的orbifold修改，证明其在局部平凡orbifold区域上具有同构性质。

边界带自交叉的解析圆盘的同构问题

The isomorphism problem for analytic discs with self-crossings on the boundary

本研究针对边界带自交叉的解析圆盘，探讨其Drury-Arveson空间限制下的乘子代数同构问题，证明同构仅由单位圆盘自同构复合映射给出，刻画了单自交叉情形的候选映射，并给出同自交叉模式下乘子代数互不同构的连续族。

Plemelj-Sokhotski isomorphism for quasicircles in Riemann surfaces and the Schiffer operator

Let $R$ be a compact Riemann surface and $Γ$ be a Jordan curve separating $R$ into connected components $Σ_1$ and $Σ_2$. We consider Calderón-Zygmund type operators $T(Σ_1,Σ_k)$ taking the space of $L^2$ anti-holomorphic one-forms on $Σ_1$ to the space of $L^2$ holomorphic one-forms on $Σ_k$, which we call the Schiffer operators. We extend results of Menahem M. Schiffer and others, which where confined to analytic Jordan curves $Γ$, to general quasicircles in a characterizing manner, and prove new identities for adjoints of the Schiffer operators. Furthermore, we show that if $V$ is the space …

Formal and convergent solutions of analytic equations

We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.

Formal biholomorphic maps of real analytic hypersurfaces

Let f : (M,p)\to (M',p') be a formal biholomorphic mapping between two germs of real analytic hypersurfaces in \C^n, p'=f(p). Assuming the source manifold to be minimal at p, we prove the convergence of the so-called reflection function associated to f. As a consequence, we derive the convergence of formal biholomorphisms between real analytic minimal holomorphically nondegenerate hypersurfaces. Related results on partial convergence of formal biholomorphisms are also obtained.