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Title: LP Curvature and the Cauchy-Riemann equation near an isolated singular point
Contributor(s): Harris, A (author)orcid ; Tonegawa, Y (author)
Publication Date: 2001
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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.
Publication Type: Journal Article
Source of Publication: Nagoya Mathematical Journal, v.164, p. 35-51
Publisher: Nagoya Daigaku, Daigakuin Tagensurikagaku Kenkyuka
Place of Publication: Japan
ISSN: 0027-7630
Field of Research (FOR): 010111 Real and Complex Functions (incl Several Variables)
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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