Semi-discrete maximal surfaces with singularities in Minkowski space
Semi-discrete maximal surfaces with singularities in Minkowski space
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闵可夫斯基空间中具有奇点的半离散极大曲面
DOI：
10.1007/978-3-030-68541-6_16
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Masashi Yasumoto
中科院分区：
文献类型：
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作者：
M. Pember;D. Polly;M. Yasumoto;山下真由子;Momonari Kudo and Shushi Harashita;Yuanyuan Bao;Toshiki Matsusaka;杉山真吾;高橋良輔;工藤桃成;Mayuko Yamashita;Naoki Endo;Masashi Yasumoto
研究了三维Minkowski空间中具有奇点的半离散极大曲面。在光滑情形下，Minkowski 3-空间中的极大曲面(平均曲率恒为0的类空曲面)具有魏尔斯特拉斯型表示，并且它们通常具有奇点。本文首先刻画了三维Minkowski空间中的半离散等温极大曲面，并给出了由可积系原理确定的半离散等温极大曲面的魏尔斯特拉斯型表示。进一步，我们证明了半离散等温极大曲面允许伴随的平均曲率保持为0的单参数族变形族。最后，我们给出了一个自然地描述这些半离散极大曲面的“奇异集”统一格式的判据，包括相应族。
We investigate semi-discrete maximal surfaces with singularities in Minkowski 3-space. In the smooth case, maximal surfaces (spacelike surfaces with mean curvature identically 0) in Minkowski 3-space admit a Weierstrass-type representation and they generally have singularities. In this paper, we first describe semi-discrete isothermic maximal surfaces in Minkowski 3-space and give a Weierstrass-type representation for them determined from integrable system principles. Furthermore, we show that semi-discrete isothermic maximal surfaces admit associated one-parameter families of deformations whose mean curvature remains identically 0. Finally we give a criterion that naturally describes the unified scheme of the “singular set” for these semi-discrete maximal surfaces, including the associated family.