Willmore deformations between minimal surfaces in $$\mathbb {H}^{n+2}$$ and $$\mathbb {S}^{n+2}$$
Willmore deformations between minimal surfaces in $$\mathbb {H}^{n+2}$$ and $$\mathbb {S}^{n+2}$$
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DOI：
10.1007/s00209-022-03169-3
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发表时间：
2022-12
影响因子：
0.8
通讯作者：
Changping Wang;Pengfu Wang
中科院分区：
文献类型：
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作者：
Changping Wang;Pengfu Wang
在本文中，我们证明了在最小曲面 in 和最小曲面 in 之间局部存在 Willmore 变形，即，存在一个光滑的 Willmore 曲面族，使得其共形等价于最小曲面 in 并且共形等价于最小曲面 in。这是曲面 M 的简单连通开子集。对于某些情况，变形是全局的。通过维罗内斯二球体的威尔莫尔变形及其推广，对于任何正数，我们在威尔莫尔能量等于的情况下构造完整的最小曲面。还提出了具有威尔莫尔能量的完整最小莫比乌斯带的示例。我们还表明，所有各向同性最小曲面都承认雅可比场与杀伤场不同，即它们不是“孤立的”。
In this paper we show that locally there exists a Willmore deformation between minimal surfaces inand minimal surfaces in, i.e., there exists a smooth family of Willmore surfacessuch thatis conformally equivalent to a minimal surface inandis conformally equivalent to a minimal surface in. Hereis a simply connected open subset of the surfaceM. For some cases the deformations are global. By the Willmore deformations of the Veronese two-sphere and its generalizations in, for any positive number, we construct complete minimal surfaces inwith Willmore energy being equal to. An example of complete minimal Möbius strip inwith Willmore energyis also presented. We also show that all isotropic minimal surfaces inadmit Jacobi fields different from Killing fields, i.e., they are not “isolated”.