On the asymptotic geometry of area-preserving maps

Geometric properties and related results for holomorphic Segre preserving maps

In this paper, we examine holomorphic Segre preserving maps between the complexifications of real hypersurfaces in $\mathbb{C}^{n+1}$. In particular, we find several sufficient conditions ensuring that Segre transversality and total Segre nondegeneracy of the maps must hold.

Volume-preserving maps between Hermitian symmetric spaces of compact type

In this paper, we establish the rigidity result for local holomorphic volume preserving maps from an irreducible Hermitian manifold of compact type into its Cartesian products.

分段保距映射讲义

Lectures on piecewise distance-preserving maps

该研究围绕二维多面体空间到平面的分段保距映射展开讨论

通过平均曲率流与Ricci流耦合变形紧致黎曼曲面间的保面积映射

Deforming area-preserving maps between surfaces by mean curvature flow coupled with Ricci flow

本文提出用归一化Ricci流演化度量、平均曲率流演化图的耦合方法变形紧致黎曼曲面间的保面积映射，证明流长期存在、保持图结构并指数收敛至极小球拉格朗日图，推广了常数量曲率情形。

关于保持(p,p)形式的hermitian流形间局部全纯映射

On local holomorphic maps between Hermitian manifolds preserving $(p,p)$-forms

本文研究了保持(p,p)形式的hermitian流形间局部全纯映射的刚性与非存在性定理。

On local holomorphic maps preserving invariant (p,p)-forms between bounded symmetric domains

Let $D, Ω_1, ..., Ω_m$ be irreducible bounded symmetric domains. We study local holomorphic maps from $D$ into $Ω_1 \times... Ω_m$ preserving the invariant $(p, p)$-forms induced from the normalized Bergman metrics up to conformal constants. We show that the local holomorphic maps extends to algebraic maps in the rank one case for any $p$ and in the rank at least two case for certain sufficiently large $p$. The total geodesy thus follows if $D=\mathbb{B}^n, Ω_i = \mathbb{B}^{N_i}$ for any $p$ or if $D=Ω_1 =...=Ω_m$ with rank$(D)\geq 2$ and $p$ sufficiently large. As a consequence, the algebrai…