Table of contents

V.S. Balaganskii and L.P. Vlasov would like to make the following corrections to their article "The problem of convexity of Chebyshev sets", the translation of which appeared in Russian Math. Surveys 51:6, pp. 1127-1190.

Contents Introduction Chapter I. Surface potentials in the Helmholtz resonator problem §1.1. Preliminary results for limiting problems §1.2. Existence of poles with small imaginary part §1.3. Representation and uniform estimates of analytic continuation in a neighbourhood of the poles §1.4. A resonator with the Dirichlet boundary conditions §1.5. Generalizations for resonators in Chapter II. Asymptotics of the poles of the Helmholtz resonator §2.1. Asymptotics of a pole in the non-degenerate case §2.2. The quasi-stationary case §2.3. Splitting of a multiple eigenvalue §2.4. The degenerate case §2.5. Asymptotics of the poles for the Dirichlet problem and for boundary-value problems in the plane

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Contents §1. Introduction §2. Some main results §3. The remainder term in the method of stationary phase (SP) §4. Elementary composite estimates of one-dimensional oscillatory integrals §5. Examples

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Contents Introduction Chapter I. Abelian varieties and theta functions §1. A condition for a complex torus to be algebraic §2. Line bundles on complex tori §3. Theta functions §4. Theta functions and maps of tori into projective spaces. Secants of Abelian varieties Chapter II. Theta functions of Riemann surfaces §5. Theta functions of Jacobi varieties §6. Theta functions of Prym varieties of double coverings with two branch points §7. Theta functions of Prym varieties of unramified coverings Chapter III. Jacobi varieties and soliton equations (the Riemann-Schottky problem, the Novikov conjecture, and trisecants) §8. Baker-Akhieser functions and rings of commuting differential operators §9. The Novikov conjecture in the Riemann-Schottky problem and trisecants of Jacobi varieties §10. The Riemann-Schottky problem Chapter IV. Prym varieties and non-linear equations §11. Soliton equations and Prym theta functions §12. Methods of finite-zone integration in the theory of the Prym map Final remarks

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