Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds

@article{Yau2011,
abstract = {Let $X_1$ and $X_2$ be two compact strongly pseudoconvex CR manifolds of dimension $2n-1\ge 5$ which bound complex varieties $V_1$ and $V_2$ with only isolated normal singularities in $\mathbb \{C\}^\{N1\}$ and $\mathbb \{C\}^\{N2\}$ respectively. Let $S_1$ and $S_2$ be the singular sets of $V_1$ and $V_2$ respectively and $S_2$ is nonempty. If $2n-N_2-1\ge 1$ and the cardinality of $S_1$ is less than 2 times the cardinality of $S_2$, then we prove that any non-constant CR morphism from $X_1$ to $X_2$ is necessarily a CR biholomorphism. On the other hand, let $X$ be a compact strongly pseudoconvex CR manifold of dimension 3 which bounds a complex variety $V$ with only isolated normal non-quotient singularities. Assume that the singular set of $V$ is nonempty. Then we prove that any non-constant CR morphism from $X$ to $X$ is necessarily a CR biholomorphism.},
author = {Yau, Stephen S.-T.},
journal = {Journal of the European Mathematical Society},
keywords = {strongly pseudoconvex CR manifold; rigidity of CR morphism; geometric genus of compact embeddable CR manifold; strongly pseudoconvex CR manifold; rigidity of CR morphism; geometric genus of compact embeddable CR manifold},
language = {eng},
number = {1},
pages = {175-184},
publisher = {European Mathematical Society Publishing House},
title = {Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds},
url = {http://eudml.org/doc/277470},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Yau, Stephen S.-T.
TI - Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 1
SP - 175
EP - 184
AB - Let $X_1$ and $X_2$ be two compact strongly pseudoconvex CR manifolds of dimension $2n-1\ge 5$ which bound complex varieties $V_1$ and $V_2$ with only isolated normal singularities in $\mathbb {C}^{N1}$ and $\mathbb {C}^{N2}$ respectively. Let $S_1$ and $S_2$ be the singular sets of $V_1$ and $V_2$ respectively and $S_2$ is nonempty. If $2n-N_2-1\ge 1$ and the cardinality of $S_1$ is less than 2 times the cardinality of $S_2$, then we prove that any non-constant CR morphism from $X_1$ to $X_2$ is necessarily a CR biholomorphism. On the other hand, let $X$ be a compact strongly pseudoconvex CR manifold of dimension 3 which bounds a complex variety $V$ with only isolated normal non-quotient singularities. Assume that the singular set of $V$ is nonempty. Then we prove that any non-constant CR morphism from $X$ to $X$ is necessarily a CR biholomorphism.
LA - eng
KW - strongly pseudoconvex CR manifold; rigidity of CR morphism; geometric genus of compact embeddable CR manifold; strongly pseudoconvex CR manifold; rigidity of CR morphism; geometric genus of compact embeddable CR manifold
UR - http://eudml.org/doc/277470
ER -