发表机构
Georgia Institute of Technology; University of South Carolina; Shanghai Jiao Tong University（佐治亚理工学院; 南卡罗来纳大学; 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
本文证明若凸曲面被固定宽度平板截取的面积仅依赖方向，则该曲面为球面，推广了布拉施克和斯塔姆的定理，并适用于光滑闭曲面，证明结合牛顿势、静电刻画及拉东变换的解析性质。
AI 中文摘要
我们证明，如果欧几里得三维空间中的一个凸曲面，被某个固定宽度的平板截下的面积仅依赖于平板的方向，则该曲面为球面。这一结果推广了布拉施克和斯塔姆的定理，后者假设了所有宽度下的平板面积性质。该结论也适用于任何光滑的闭嵌入曲面。证明基于一个平均恒等式，该恒等式将平板面积与曲面的牛顿势联系起来，结合门德斯和赖歇尔的球面静电刻画，以及拉东变换的解析微局域性质，后者用于证明平板面积性质迫使实解析性，依据柏原和博曼的定理。
英文摘要
We show that a convex surface in Euclidean 3-space is a sphere if the area cut off from it by a slab of some fixed width depends only on the direction of the slab. This result generalizes theorems of Blaschke and Stamm, which assumed the slab-area property for every width. It holds also for any smooth closed embedded surface. The proof is based on an averaging identity, which relates slab areas to the Newtonian potential of the surface, the electrostatic characterization of spheres by Mendez and Reichel, and analytic microlocal properties of the Radon transform, which are used to show that the slab-area property forces real analyticity, via theorems of Kashiwara and Boman.
Comments15 pages
