球空间中超曲面的共形平均曲率流的爆破
The Blow-Up of the Conformal MeanCurvature Flow Hypersurfaces inSpherical Spaces
DOI: 10.12677/PM.2025.1511280, PDF,    国家自然科学基金支持
作者: 张斌, 刘建成*：西北师范大学数学与统计学院，甘肃兰州
关键词: 共形平均曲率流；第二基本形式；爆破； Conformal Mean Curvature Flow； The Second Fundamental Form； Blow-Up
摘要: 本文讨论了球空间中超曲面的共形平均曲率流，得到了球空间中超曲面在共形平均曲率流下的爆破定理，即任何紧致超曲面的第二基本形式平方范数的最大值在有限时间内趋于无穷。
Abstract: This paper discusses the conformal mean curvature ow for hypersurfaces in spherical space and obtains a blow-up theorem for hypersurfaces in spherical space under the conformal mean curvature ow, that is, the maximum of the squared norm of the second fundamental form of any compact hypersurface tends to infinity in finite time.
文章引用：张斌, 刘建成. 球空间中超曲面的共形平均曲率流的爆破[J]. 理论数学, 2025, 15(11): 178-195. https://doi.org/10.12677/PM.2025.1511280

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