The Linearized Calderón Problem on Complex Manifolds
Year of publication
2019
Authors
Guillarmou, Colin; Salo, Mikko; Tzou, Leo
Abstract
In this note we show that on any compact subdomain of a K¨ahler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to the linearized anisotropic Calder´on problem on a class of complex manifolds that includes compact subdomains of Stein manifolds and sufficiently small subdomains of K¨ahler manifolds. Some of these manifolds do not admit limiting Carleman weights, and thus cannot be treated by standard methods for the Calder´on problem in higher dimensions. The argument is based on constructing Morse holomorphic functions with approximately prescribed critical points. This extends earlier results from the case of Riemann surfaces to higher dimensional complex manifolds.
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Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Journal
Publisher
Volume
35
Issue
6
Pages
1043-1056
ISSN
Publication forum
Publication forum level
1
Open access
Open access in the publisher’s service
No
Self-archived
Yes
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object],[object Object]
Publication country
Germany
Internationality of the publisher
International
Language
English
International co-publication
Yes
Co-publication with a company
No
DOI
10.1007/s10114-019-8129-7
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes