论文标题
通过双曲线log-convex密度猜想，在$ h^m _ {\ mathbb {c}} $中接近等级问题
Approaching the isoperimetric problem in $H^m_{\mathbb{C}}$ via the hyperbolic log-convex density conjecture
论文作者
论文摘要
我们证明，以某个基点为中心的地理球是在实际双曲线空间中等二的，$ h _ {\ mathbb r}^n $在体积和周长上具有光滑，径向，严格的log-convex密度。这是G. R. Chambers对$ \ Mathbb r^n $的log-convex密度的结果的类似物。作为一种应用，我们证明，在任何等级中，一个非紧缩类型的对称空间，在一类享受合适的径向对称性概念的集合中，测地球是等等的。
We prove that geodesic balls centered at some base point are isoperimetric in the real hyperbolic space $H_{\mathbb R}^n$ endowed with a smooth, radial, strictly log-convex density on the volume and perimeter. This is an analogue of the result by G. R. Chambers for log-convex densities on $\mathbb R^n$. As an application we prove that in any rank one symmetric space of non-compact type, geodesic balls are isoperimetric in a class of sets enjoying a suitable notion of radial symmetry.
