NEAR OPTIMAL BOUNDS IN FREIMAN'S THEOREM

CALDERÓN INVERSE PROBLEM ON RIEMANN SURFACES 119
[10] L. D. FADDEEV, Increasing solutions of the Schrödinger equation (in Russian), Dokl.
Akad. Nauk SSSR 165 (1965), 514 – 517; English translation in Sov. Phys. Dokl.
10 (1966), 1033 – 1035. 85, 100
[11] H. M FARKAS and I. KRA, Riemann Surfaces, 2nd ed., Grad. Texts in Math. 71,
Springer, New York, 1992. MR 1139765 86
[12] I. M. GELFAND, “Some aspects of functional analysis and algebra” in Proceedings of
the International Congress of Mathematicians (Amsterdam, 1954),
North-Holland, Amsterdam, 253 – 276. MR 0095423 83
[13] C. R. GRAHAM and M. ZWORSKI, Scattering matrix in conformal geometry, Invent.
Math. 152 (2003), 89 – 118. MR 1965361 111
[14] C. GUILLARMOU and L. GUILLOPÉ, The determinant of the Dirichlet-to-Neumann map
for surfaces with boundary, Int. Math. Res. Not. IMRN 2007, no. 22, art. ID
rnm099. MR 2376211 111
[15] C. GUILLARMOU and A. SÁ BARRETO, Inverse problems for Einstein manifolds,
Inverse Probl. Imaging 3 (2009), 1 – 15. MR 2558301 84
[16] C. GUILLARMOU and L. TZOU,“Calderón inverse problem for the Schrödinger
operator on Riemann surfaces” in The AMSI-ANU Workshop on Spectral Theory
and Harmonic Analysis (Canberra, 2009), Proc. Centre Math. Appl. Austral. Nat.
Univ. 44, Austral. Nat. Univ., Canberra, 2010, 129 – 141. MR 2655386 84
[17] G. HENKIN and V. MICHEL, Inverse conductivity problem on Riemann surfaces, J.
Geom. Anal. 18 (2008), 1033 – 1052. MR 2438910 84, 85
[18] G. HENKIN and R. G. NOVIKOV, On the reconstruction of conductivity of bordered
two-dimensional surface in R 3 from electrical currents measurements on its
boundary, to appear in J. Geom. Anal., preprint, arXiv:1003.4897v1 [math.AP]
85
[19] O. Y. IMANUVILOV, G. UHLMANN, andM. YAMAMOTO, The Calderón problem with
partial data in two dimensions, J.Amer.Math.Soc.23 (2010), 655 – 691. 84, 85,
86, 95, 96, 103, 105
[20] M. S. JOSHI and A. SÁ BARRETO, Inverse scattering on asymptotically hyperbolic
manifolds, Acta Math. 184 (2000), 41 – 86. MR 1756569
[21] C. E. KENIG, J. SJÖSTRAND,andG. UHLMANN, The Calderón problem with partial
data, Ann. of Math. (2) 165 (2007), 567 – 591. MR 2299741 111 84
[22] R. KOHN and M. VOGELIUS, Determining conductivity by boundary measurements,
Comm. Pure Appl. Math. 37 (1984), 289 – 298. MR 0739921 114
[23] M. LASSAS, M. TAYLOR,andG. UHLMANN, The Dirichlet-to-Neumann map for
complete Riemannian manifolds with boundary, Comm. Anal. Geom. 11 (2003),
207 – 222. MR 2014876 84
[24] M. LASSAS and G. UHLMANN, On determining a Riemannian manifold from the
Dirichlet-to-Neumann map. Ann. Sci. Éc. Norm. Supér. (4) 34 (2001), 771 – 787.
MR 1862026 84
[25] R. MAZZEO and M. TAYLOR, Curvature and uniformization, Israel J. Math. 130 (2002),
323 – 346. MR 1919383 95
[26] D. MCDUFF and D. SALAMON, J -Holomorphic curves and symplectic topology, Amer.
Math. Soc. Colloq. Publ. 52, Amer. Math. Soc., Providence, 2004. MR 2045629
87, 88