Harris, A; Tonegawa, Y

Author(s)

Harris, A

Tonegawa, Y

Publication Date

2001

Abstract

Let X be a complex n-dimensional reduced analytic space with isolated singular point x0,and with a strongly plurisubharmonic function p : X --> [0;∞) such that p(x0) = 0.A smooth Kähler form on X {x0} is then defined by i p.The associated metric is assumed to have Lnloc-curvature, toadmit the Sobolev inequality and to have suitable volume growth near x0.Let E --> X {x0} be a Hermitian-holomorphic vector bundle, and ξ a smooth (0,1)-form with coefficients in E.The main result of this article states that if ξ and the curvature of E are both Lnloc,then the equation ∂u = ξ has a smooth solution on a punctured neighbourhood of x0.Applications of this theorem to problems of holomorphic extension, and in particular a result of Kohn-Rossi type for sections over a CR-hypersurface, are discussed in the final section.

Citation

Nagoya Mathematical Journal, v.164, p. 35-51

ISSN

0027-7630

Link

https://hdl.handle.net/1959.11/1055

Publisher

Nagoya Daigaku, Daigakuin Tagensurikagaku Kenkyuka

Title

LP Curvature and the Cauchy-Riemann equation near an isolated singular point

Type of document

Journal Article

Entity Type

Publication

<i>L<sup>P</sup></i> Curvature and the Cauchy-Riemann equation near an isolated singular point

Files:

Author(s)	Harris, A Tonegawa, Y
Publication Date	2001
Abstract	Let <i>X</i> be a complex <i>n</i>-dimensional reduced analytic space with isolated singular point <i>x</i><sub>0</sub>,and with a strongly plurisubharmonic function <i>p</i> : <i>X</i> --> [0;∞) such that <i>p</i>(<i>x</i><sub>0</sub>) = 0.A smooth Kähler form on <i>X</i> {<i>x</i><sub>0</sub>} is then defined by i <i>p</i>.The associated metric is assumed to have <i>L</i><sup>n</sup><sub>loc</sub>-curvature, toadmit the Sobolev inequality and to have suitable volume growth near <i>x</i><sub>0</sub>.Let <i>E</i> --> <i>X</i> {<i>x</i><sub>0</sub>} be a Hermitian-holomorphic vector bundle, and ξ a smooth (0,1)-form with coefficients in <i>E</i>.The main result of this article states that if ξ and the curvature of <i>E</i> are both <i>L</i><sup>n</sup><sub>loc</sub>,then the equation ∂<i>u</i> = ξ has a smooth solution on a punctured neighbourhood of <i>x</i><sub>0</sub>.Applications of this theorem to problems of holomorphic extension, and in particular a result of Kohn-Rossi type for sections over a <i>CR</i>-hypersurface, are discussed in the final section.
Citation	Nagoya Mathematical Journal, v.164, p. 35-51
ISSN	0027-7630
Link	https://hdl.handle.net/1959.11/1055
Publisher	Nagoya Daigaku, Daigakuin Tagensurikagaku Kenkyuka
Title	<i>L<sup>P</sup></i> Curvature and the Cauchy-Riemann equation near an isolated singular point
Type of document	Journal Article
Entity Type	Publication