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

Salo, Mikko

Publication details

All authors or editors: Guillarmou, Colin; Salo, Mikko; Tzou, Leo

Journal or series: Acta Mathematica Sinica

ISSN: 1439-8516

eISSN: 1439-7617

Publication year: 2019

Volume: 35

Issue number: 6

Pages range: 1043-1056

Publisher: Springer

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s10114-019-8129-7

Publication open access: Other 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 available: https://hal.archives-ouvertes.fr/hal-01827890v1

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.

Keywords: inverse problems; partial differential equations; manifolds (mathematics)

Free keywords: inverse problem; Calderón problem; complex manifold

Fields of science: