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

常平均曲率曲面的性质及其完备性、紧性、有界第二基本形式和连通性的假设。目前，我正在证明具有有界第二基本形式的单连通、完备、常平均曲率曲面是紧致的或不包含在外在球中的。我使用的技术来自我的导师的论文和类似的结果，只有最小的表面。我们研究嵌入在欧几里得和非欧几里得空间中的CMC超曲面，它们具有有界的第二基本形式、非紧致和完全。

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.