渐近局部双曲流形中的凸包与面积极小化流
Convex hulls and area minimizing currents in asymptotically locally hyperbolic manifolds
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中文总结 AI 辅助
该研究在无全局曲率假设的共形紧化渐近局部双曲流形中，通过构造共形无穷远处的障碍凸包，推广Anderson的双曲空间定理，求解任意余维数整电流的定向渐近普拉托问题。
中文摘要 AI 辅助
我们在无全局曲率假设的共形紧化渐近局部双曲流形中，求解任意余维数整电流的定向渐近普拉托问题，这推广了Anderson在双曲空间中的定理。新的关键要素是在共形无穷远处构造障碍凸包，其可作为面积极小化电流与稳定变分体的障碍；在共形紧化情形下，相关凸包等式将Anderson的结果推广到全局捏缩负曲率之外的情形。
英文摘要
We solve the oriented asymptotic Plateau problem for integral currents of arbitrary codimension in conformally compact asymptotically locally hyperbolic manifolds without global curvature assumptions. This extends Anderson's theorem in hyperbolic space. A new ingredient is the construction of a barrier hull near conformal infinity, which serves as a barrier for area minimizing currents and stationary varifolds. In the conformally compact setting, the associated convex hull identity extends Anderson's result beyond globally pinched negative curvature.
发表机构
- University of Connecticut（康涅狄格大学）
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