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Geometric properties of solutions of the Levi-equation. (English) Zbl 0681.35017
Given a smooth real hypersurface M in \({\mathbb{C}}^ 2\) the Levi curvature k is defined. In the case when M is the graph of a function \(u(u_ 1,u_ 2,u_ 3)\) \((z_ 1=x_ 1+ix_ 2\), \(z_ 2=x_ 3+ix_ n)\) then u satisfies, in terms of k, a second order quasilinear elliptic degenerate equation \(L(k;u)=0\) called the Levi equation. In the paper geometric properties of smooth solutions of \(L(k;u)=0\) are discussed.
Reviewer: G.Tomassini

35B99 Qualitative properties of solutions to partial differential equations
53B99 Local differential geometry
35J70 Degenerate elliptic equations
Full Text: DOI
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