The Linearized Calderón Problem on Complex Manifolds
Guillarmou, C., Salo, M., & Tzou, L. (2019). The Linearized Calderón Problem on Complex Manifolds. Acta Mathematica Sinica, 35(6), 1043-1056. https://doi.org/10.1007/s10114-019-8129-7
Published inActa Mathematica Sinica
© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019.
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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Related funder(s)Academy of Finland; European Commission
Funding program(s)Academy Project, AoF; Centre of Excellence, AoF; FP7 (EU's 7th Framework Programme)
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingThe first author is partially supported by ERC Consolidator Grant IPFLOW (Grant No. 725967), the second author was supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Problems Research (Grant Nos. 284715 and 309963)) and by the European Research Council under FP7/2007–2013 ERC StG (Grant No. 307023) and Horizon 2020 ERC CoG (Grant No. 770924), and the third author is partially supported by Australian Research Council (Grant Nos. DP190103302 and DP190103451) ...
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