A1 Journal article (refereed)
The Linearized Calderón Problem on Complex Manifolds (2019)

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

JYU authors or editors

Publication details

All authors or editorsGuillarmou, Colin; Salo, Mikko; Tzou, Leo

Journal or seriesActa Mathematica Sinica



Publication year2019


Issue number6

Pages range1043-1056


Publication countryGermany

Publication languageEnglish


Publication open accessOther way freely accessible online

Publication channel open access

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/64239

Web address where publication is availablehttps://hal.archives-ouvertes.fr/hal-01827890v1


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.

Keywordsinverse problemspartial differential equationsmanifolds (mathematics)

Free keywordsinverse problem; Calderón problem; complex manifold

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Ministry reportingYes

Reporting Year2019

JUFO rating1

Last updated on 2024-11-05 at 20:47