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December 2002 Cauchy-Riemann orbifolds
Sorin Dragomir, Jun Masamune
Tsukuba J. Math. 26(2): 351-386 (December 2002). DOI: 10.21099/tkbjm/1496164430


For any $CR$ orbifold $B$, of $CR$ dimension $n$, we build a vector bundle (in the sense of J. Girbau & M. Nicolau, [13]) $T_{1,0}(B)$ over $B$, so that $T_{1,0}(B)_{p} \approx \bm{C}^{n}/G_{x}$ at any singular point $p=\varphi(x)\in B$ (and the portion of $T_{1,0}(B)$ over the regular part of $B$ is an ordinary $CR$ stmcture), hence study the tangential Cauchy--Riemann equations on orbifolds. As an application, we build a two-sided parametrix for for the Kohn--Rossi laplacian $\Box_{\Omega}$ (on the domain $\Omega$ of a local uniformizing system $\{\Omega, G, \varphi\}$ of $B$) inverting $\Box_{\Omega}$ over the $G$-invariant $(0, q)$-forms $(1 \leq q \leq n-1)$ up to (smoothing) operators of type $1$ (in the sense of G. B. Folland & E. M. Stein, [12]).


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Sorin Dragomir. Jun Masamune. "Cauchy-Riemann orbifolds." Tsukuba J. Math. 26 (2) 351 - 386, December 2002.


Published: December 2002
First available in Project Euclid: 30 May 2017

zbMATH: 1023.32021
MathSciNet: MR1940400
Digital Object Identifier: 10.21099/tkbjm/1496164430

Rights: Copyright © 2002 University of Tsukuba, Institute of Mathematics


Vol.26 • No. 2 • December 2002
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