A Burns-Krantz type theorem for domains with corners

Non-tangential Burns-Krantz rigidity

We prove some non-tangential Burns-Krantz type boundary rigidity theorems.

The Burns-Krantz rigidity with an interior fixed point

We prove a Burns-Krantz type boundary rigidity near strongly pseudoconvex points for holomorphic self-maps with an interior fixed point. This confirms a conjecture of Huang.

非光滑域中的Burns-Krantz刚性

Burns-Krantz rigidity in non-smooth domains

本文研究非光滑域中复测地线的正则性现象，证明了Burns-Krantz刚性定理，并探讨了有界对称域上的应用可能性。

Another look at the Burns-Krantz Theorem

We obtain a generalization of the Burns-Krantz rigidity theorem for holomorphic self-mappings of the unit disk in the spirit of the classical Schwarz-Pick Lemma and its continuous version due to L.Harris via the generation theory for one-parameter semigroups. In particular, we establish geometric and analytic criteria for a holomorphic function on the disk with a boundary null point to be a generator of a semigroup of linear fractional transformations under some relations between three boundary derivatives of the function at this point.

Blaschke乘积的Burns-Krantz型定理

A Burns-Krantz type theorem for Blaschke products

该研究针对将单位圆盘映射到自身的全纯函数，建立了Burns-Krantz型边界Schwarz引理，并给出充分条件使函数成为具有预定临界点的Blaschke乘积，证明依赖Nehari加强的局部Julia型不等式。

Rigidity of Analytic Functions at the Boundary

A new elementary proof for a theorem of D. Burns and S. Krantz on the rigidity of the analytic self maps of the unit disc was recently discovered by L. Baracco, D. Zaitsev, and G. Zampieri. We use their argument to generalize Burns-Krantz theorems on the unit disc and on the unit ball of ${\mathbb C}^n$.