Differential and Integral Equations

A symmetry result on Reinhardt domains

Vittorio Martino

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Abstract

We show the following symmetry property of a bounded Reinhardt domain $\Omega$ in $\mathbb{C}^{n+1}$: let $M=\partial\Omega$ be the smooth boundary of $\Omega $ and let $h$ be the Second Fundamental Form of $M$; if the coefficient $h(T,T)$ related to the characteristic direction $T$ is constant then $M$ is a sphere. In the Appendix we state the result from a hamiltonian point of view.

Article information

Source
Differential Integral Equations, Volume 24, Number 5/6 (2011), 495-504.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356018915

Mathematical Reviews number (MathSciNet)
MR2809618

Zentralblatt MATH identifier
1249.32022

Subjects
Primary: 53A05: Surfaces in Euclidean space 32V15: CR manifolds as boundaries of domains

Citation

Martino, Vittorio. A symmetry result on Reinhardt domains. Differential Integral Equations 24 (2011), no. 5/6, 495--504. https://projecteuclid.org/euclid.die/1356018915


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