]. P. An17 and . Angulo-ardoy, On the set of metrics without local limiting Carleman weights, Inverse Probl. Imaging, vol.11, pp.47-64, 2017.

P. Angulo-ardoy, D. Faraco, and L. Guijarro, SUFFICIENT CONDITIONS FOR THE EXISTENCE OF LIMITING CARLEMAN WEIGHTS, Forum of Mathematics, Sigma, vol.32, p.7, 2017.
DOI : 10.3934/ipi.2017003

P. Angulo-ardoy, D. Faraco, L. Guijarro, and A. Ruiz, Obstructions to the existence of limiting Carleman weights, Analysis & PDE, vol.60, issue.3, pp.575-595, 2016.
DOI : 10.1103/PhysRevLett.26.1656

]. A. Bu08 and . Bukhgeim, Recovering a potential from Cauchy data in the twodimensional case, J. Inverse Ill-posed Probl, vol.16, pp.19-34, 2008.

]. A. Ca80 and . Calderón, On an inverse boundary value problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, 1980.

[. Ferreira, C. E. Kenig, and M. Salo, Determining an Unbounded Potential from Cauchy Data in Admissible Geometries, Communications in Partial Differential Equations, vol.88, issue.1, pp.50-68, 2013.
DOI : 10.1088/0266-5611/25/12/123011

URL : https://hal.archives-ouvertes.fr/hal-01286017

D. Ferreira, C. E. Kenig, M. Salo, and G. Uhlmann, Limiting Carleman weights and anisotropic inverse problems, Inventiones mathematicae, vol.41, issue.1, pp.119-171, 2009.
DOI : 10.1007/978-1-4757-6434-5

D. Ferreira, Y. Kurylev, M. Lassas, and M. Salo, The Calder??n problem in transversally anisotropic geometries, Journal of the European Mathematical Society, vol.18, issue.11, pp.2579-2626, 2016.
DOI : 10.4171/JEMS/649

[. Ferreira, Y. Kurylev, M. Lassas, T. Liimatainen, and M. Salo, The linearized Calderón problem in transversally anisotropic geometries, https://arxiv.org/abs/1712, 04716. [Fo11] F. Forstneric, Stein manifolds and holomorphic mappingsGS09] C. Guillarmou, A. Sá Barreto, Inverse problems for Einstein manifolds, pp.1-15, 2009.

L. [. Guillarmou and . Tzou, Calderón inverse problem for the Schrödinger operator on Riemann surfaces, The AMSI-ANU Workshop on Spectral Theory and Harmonic Analysis inverse problem with partial data on Riemann surfaces, Duke Math, Proc. Centre Math. Appl. Austral. Nat. Univ. Austral. Nat. Univ. J, vol.44, issue.158, pp.129-141, 2011.

L. [. Guillarmou, O. Tzou, G. Imanuvilov, M. Uhlmann, and . Yamamoto, The Calderón inverse problem in two dimensions Complex geometry ? an introduction The Calderón problem with partial data in two dimensions, Inverse Problems and Applications: Inside Out II (edited by G. Uhlmann), MSRI Publications 60, pp.119-166, 2005.

M. [. Kenig and . Salo, The Calder??n problem with partial data on manifolds and applications, Analysis & PDE, vol.138, issue.8, pp.2003-2048, 2013.
DOI : 10.1090/gsm/138

M. [. Kenig and . Salo, Recent progress in the Calder??n problem with partial data, Contemp. Math, pp.615-193, 2014.
DOI : 10.1090/conm/615/12245

URL : https://jyx.jyu.fi/bitstream/123456789/56803/1/salorecentprogressinthe.pdf

C. E. Kenig, M. Salo, and G. Uhlmann, Inverse problems for the anisotropic Maxwell equations, Duke Math, J, vol.157, pp.369-419, 2011.
DOI : 10.1215/00127094-1272903

URL : http://arxiv.org/pdf/0905.3275

C. E. Kenig, M. Salo, and G. Uhlmann, Reconstructions from boundary measurements on admissible manifolds, Inverse Problems and Imaging, vol.5, issue.4, pp.859-877, 2011.
DOI : 10.3934/ipi.2011.5.859

URL : https://doi.org/10.3934/ipi.2011.5.859

C. E. Kenig, J. Sjöstrand, and G. Uhlmann, The Calder??n problem with partial data, Annals of Mathematics, vol.165, issue.2, pp.567-591, 2007.
DOI : 10.4007/annals.2007.165.567

M. Lassas, M. Taylor, and G. Uhlmann, The Dirichlet-to-Neumann map for complete Riemannian manifolds with boundary, Communications in Analysis and Geometry, vol.11, issue.2, pp.207-221, 2003.
DOI : 10.4310/CAG.2003.v11.n2.a2

G. [. Lassas and . Uhlmann, On determining a Riemannian manifold from the Dirichlet-to-Neumann map, Annales Scientifiques de l'??cole Normale Sup??rieure, vol.34, issue.5, pp.771-787, 2001.
DOI : 10.1016/S0012-9593(01)01076-X

M. [. Liimatainen and . Salo, Nowhere conformally homogeneous manifolds and limiting Carleman weights, Inverse Probl. Imaging, vol.6, pp.523-530, 2012.

]. A. Mo07 and . Moroianu, Lectures on Kähler geometry Student Texts 69 [Na96] A. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math, pp.143-71, 1996.

G. [. Sjöstrand and . Uhlmann, Local analytic regularity in the linearized Calder??n problem, Analysis & PDE, vol.95, issue.3, pp.515-544, 2016.
DOI : 10.1088/0266-5611/25/12/123011

G. [. Sylvester and . Uhlmann, A Global Uniqueness Theorem for an Inverse Boundary Value Problem, The Annals of Mathematics, vol.125, issue.1, pp.153-169, 1987.
DOI : 10.2307/1971291

]. K. Uh76 and . Uhlenbeck, Generic properties of eigenfunctions, Amer, J. Math, vol.98, pp.1059-1078, 1976.

]. G. Uh14 and . Uhlmann, Inverse problems: seeing the unseen, Bull. Math. Sci, vol.4, pp.209-279, 2014.

, France E-mail address: cguillar@math.cnrs.fr University of Jyvaskyla, Department of Mathematics and Statistics, PO Box 35, 40014 University of Jyvaskyla, Finland E-mail address: mikko, j.salo@jyu.fi School of Mathematics and Statistics