关于高维凸体的Bezdek猜想及其对称中心
On Bezdek's conjecture for high-dimensional convex bodies with an aligned center of symmetry
AI总结：
本文在高维空间中验证了Bezdek猜想，假设通过固定点的截面具有反射轴，且互补不变子空间平行于固定超平面，证明了在正交和仿射设置中成立。
摘要：
1999年，K. Bezdek提出猜想，认为在$\mathbb R^3$中，所有平面截面都有反射轴的凸体是椭球体和旋转体。本文在任意维度$n\geq 3$中证明了该猜想，仅假设通过固定点的截面具有反射轴，并且互补不变子空间都平行于固定超平面。结果在正交和仿射设置中均成立。
英文摘要：
In 1999, K. Bezdek posed a conjecture stating that among all convex bodies in $\mathbb R^3$, ellipsoids and bodies of revolution are characterized by the fact that all their planar sections have an axis of reflection. We prove Bezdek's conjecture in arbitrary dimension $n\geq 3$, assuming only that sections passing through a fixed point have an axis of reflection, provided that the complementary invariant subspaces are all parallel to a fixed hyperplane. The result is proven in both orthogonal and affine settings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
