An inverse approach to hyperspheres of prescribed mean curvature in Euclidean space. (English) Zbl 1498.53007
Summary: We construct families of smooth functions \(H: \mathbb{R}^{n+1} \rightarrow \mathbb{R}\) such that the Euclidean \((n + 1)\)-space is completely filled by not necessarily round hyperspheres of mean curvature \(H\) at every point.
MSC:
| 53A07 | Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces |
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
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