On the geometry of CMC hyper surfaces embedded in a manifold of dimension 4 or 5

嵌入 4 维或 5 维流形的 CMC 超曲面几何

• 批准号: 2289230
• 金额: --
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2289230
• 关键词: geometry; CMC; hyper; surfaces; embedded

Properties of constant mean curvature surfaces, with assumptions on completeness, compactness, bounded second fundamental form and connectedness. Currently, I am proving that a simply connected, complete, constant mean curvature surface with bounded second fundamental form is either compact or not contained in an extrinsic ball. I am using techniques from my supervisor's paper and from similar results that are for minimal surfaces only.We are investigating CMC hypersurfaces embedded in Euclidean and non-Euclidean space which have bounded second fundamental form, are non-compact and are complete.

常平均曲率曲面的性质，在完备性、紧性、有界第二基本形式和连通性的假设下。目前，我证明了一个简单的连接，完整的，恒定的平均曲率曲面与有界的第二基本形式是紧凑的或不包含在一个外在的球。我使用的技术从我的导师的文件和类似的结果是极小surfacesonly.We调查CMC超曲面嵌入在欧几里德和非欧几里德空间有界的第二基本形式，是非紧的，是完整的。