A symmetry result on Reinhardt domains

2010/11/18 by Vittorio Martino, Martino, Vittorio
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1011.4119

arxiv created 2010/11/21 · arxiv updated 2010/11/23

Abstract

We show the following symmetry property of a bounded Reinhardt domain Ω in ℂⁿ⁺¹: let M=∂Ω be the smooth boundary of Ω 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 Appendix we state the result from an hamiltonian point of view.

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