发表机构
Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立无曲率假设的完备黎曼流形体积估计，证明欧几里得空间中一类可定向超曲面（含 $Q_k$-流自收缩子和特定极小超曲面）具有至多多项式体积增长和有限加权体积。
AI 中文摘要
本文在涉及一个正常函数和对称张量的适当微分不等式下，建立了完备黎曼流形的一般体积估计，无需施加曲率假设。作为应用，我们证明了欧几里得空间中适当浸入的一类可定向超曲面具有至多多项式体积增长和有限加权体积。该类特别包括 $Q_k$-流的某些自收缩子以及位置向量法向分量有界的适当浸入极小超曲面。
英文摘要
In this paper, we establish a general volume estimate for complete Riemannian manifolds under suitable differential inequalities involving a proper function and a symmetric tensor, without imposing curvature assumptions. As an application, we prove that a class of orientable hypersurfaces properly immersed in Euclidean space has at most polynomial volume growth and finite weighted volume. This class includes, in particular, certain self-shrinkers of the $Q_k$-flow and properly immersed minimal hypersurfaces for which the normal component of the position vector is bounded.
Comments22 pages. All comments are welcome
