发表机构
Great Bay University; Shanghai Jiao Tong University（大湾区大学; 上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对几何受限的面积极小化可求积流建立与余维数无关的质量界，解决了Lin内部质量界问题，还改进了双曲空间相关边界正则性结果。
AI 中文摘要
我们针对几何受限的面积极小化可求积流，建立了与余维数无关的质量界。在欧氏空间中，我们结合Colding-Minicozzi的受限体积加倍定理与流形理论的挤压论证，对每个代数重数Q，给出了Lin内部质量界问题的肯定回答：内部质量由C(n)Q界定，且无需在更大尺度上施加先验质量界。对于双曲空间的应用，我们在全测地的ℍⁿ副本的细管状邻域中，对固定尺度论证进行曲率修正，将此辅助估计与局部挤压估计结合，消除了文献[13]边界正则性结果中双指数局部质量增长条件。
英文摘要
We establish codimension-independent mass bounds for geometrically confined area-minimizing rectifiable currents. In Euclidean space, we combine the confined-volume doubling theorem of Colding--Minicozzi with a current-theoretic squashing argument. This gives an affirmative answer to Lin's interior mass-bound problem for every algebraic projection multiplicity $Q$: the interior mass is bounded by $C(n)Q$, without an a priori mass bound at a larger scale. This result yields a degree-one Bernstein-type rigidity result under sublinear confinement. For the hyperbolic application, we make the curvature modification of the fixed-scale argument needed in a thin tubular neighborhood of a totally geodesic copy of $\mathbb{H}^n$. Combining this auxiliary estimate with a localized squashing estimate removes the doubly exponential local mass-growth condition from the boundary regularity results in [13].
CommentsWe included some basic applications of the main theorem
