Minkowski Inequality in Cartan–Hadamard Manifolds
Minkowski Inequality in Cartan–Hadamard Manifolds
复制标题
Cartan-Hadamard 流形中的闵可夫斯基不等式
DOI：
10.1093/imrn/rnad114
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发表时间：
2023
影响因子：
1
通讯作者：
Spruck, Joel
中科院分区：
文献类型：
--
作者：
Ghomi, Mohammad;Spruck, Joel
利用调和平均曲率流，建立了Cartan-Hadamard-流形中给定面积的凸曲面的总平均曲率的Minkowski型下界.这个不等式也改进了双曲空间中总平均曲率的已知估计。作为应用，利用全平均曲率的单调性结果，得到了非正曲空间中距离函数为凸函数的曲面的Bonnesen型等周不等式。闵可夫斯基不等式和等周不等式之间的这种联系被推广到任意维的Cartan-Hadamard流形。
Using harmonic mean curvature flow, we establish a sharp Minkowski-type lower bound for total mean curvature of convex surfaces with a given area in Cartan-Hadamard-manifolds. This inequality also improves the known estimates for total mean curvature in hyperbolic-space. As an application, we obtain a Bonnesen-style isoperimetric inequality for surfaces with convex distance function in nonpositively curved-spaces, via monotonicity results for total mean curvature. This connection between the Minkowski and isoperimetric inequalities is extended to Cartan–Hadamard manifolds of any dimension.