A characterization of ellipsoids and balls in 𝐶ⁿ

Ligocka, Ewa

doi:10.1090/S0002-9939-1990-1000159-5

A characterization of ellipsoids and balls in $\textbf {C}^ n$
HTML articles powered by AMS MathViewer

by Ewa Ligocka PDF

Proc. Amer. Math. Soc. 110 (1990), 103-107 Request permission

Abstract:

The following fact is proved: If $D$ is a smooth bounded domain in ${{\mathbf {C}}^n}$ for which Bergman and Szegö projections are equal on smooth harmonic functions then $D$ is a ball.

References

David E. Barrett, Irregularity of the Bergman projection on a smooth bounded domain in $\textbf {C}^{2}$, Ann. of Math. (2) 119 (1984), no. 2, 431–436. MR 740899, DOI 10.2307/2007045
Steven R. Bell, A duality theorem for harmonic functions, Michigan Math. J. 29 (1982), no. 1, 123–128. MR 646379
Ewa Ligocka, The Bergman projection on harmonic functions, Studia Math. 85 (1987), no. 3, 229–246. MR 887486, DOI 10.4064/sm-85-3-229-246

Integral identities and symmetry

Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
James Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal. 43 (1971), 304–318. MR 333220, DOI 10.1007/BF00250468
H. F. Weinberger, Remark on the preceding paper of Serrin, Arch. Rational Mech. Anal. 43 (1971), 319–320. MR 333221, DOI 10.1007/BF00250469