On the Lu Qi-keng conjecture
HTML articles powered by AMS MathViewer
- by Nobuyuki Suita and Akira Yamada PDF
- Proc. Amer. Math. Soc. 59 (1976), 222-224 Request permission
Abstract:
We shall give a complete answer to the Lu Qi-keng conjecture for finite Riemann surfaces. Our result is that every finite Riemann surface which is not simply-connected is never a Lu Qi-keng domain, i.e. the Bergman kernel $K(z,t)$ of it has zeros for suitable $t$’s.References
- Q.-k. Lu, On Kaehler manifolds with constant curvature, Chinese Math.–Acta 8 (1966), 283–298. MR 0206990
- Paul Rosenthal, On the zeros of the Bergman function in doubly-connected domains, Proc. Amer. Math. Soc. 21 (1969), 33–35. MR 239066, DOI 10.1090/S0002-9939-1969-0239066-3
- Menahem Schiffer, The kernel function of an orthonormal system, Duke Math. J. 13 (1946), 529–540. MR 19115
- M. Skwarczyński, The invariant distance in the theory of pseudoconformal transformations and the Lu Qi-keng conjecture, Proc. Amer. Math. Soc. 22 (1969), 305–310. MR 244512, DOI 10.1090/S0002-9939-1969-0244512-5
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 59 (1976), 222-224
- MSC: Primary 32H10; Secondary 30A31
- DOI: https://doi.org/10.1090/S0002-9939-1976-0425185-9
- MathSciNet review: 0425185