Spacelike hypersurfaces of constant \(r\)th \(F\)-mean curvature with light-like boundary. (Chinese. English summary) Zbl 07828149
Summary: Let \(\overline{W}_{F(t)}\), corresponding to a rotation invariant function \(F(t(\nu))\) with a convexity condition on the upper hyperboloid \(\mathbb{H}_+^n\), be a compact space-like Wulff shape bounded by a light-like \((n-1)\)-round sphere. By applying perturbation metric and some integral formulae, we show that the only spacelike hypersurface with constant \(r\)th \(F\)-mean curvature in \(\mathbb{L}^{n+1}\), which is tangent to \(\overline{W}_{F(t)}\) on the boundary, is the Wulff shape.
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53A30 | Conformal differential geometry (MSC2010) |
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