2026/07/21 by Zhijie Chen, Changfeng Gui, Shihong Zhang
#math.DG
In this paper, using a limiting approach, we establish a new type of weighted Carleman inequality in all dimensions n≥ 2 and classify all extremal functions. In particular, when n=2, we prove that our inequality is equivalent to a sharp norm inequality in the Bergman space. In even dimensions, we further establish a sharp weighted Huber isoperimetric inequality on the unit ball, which generalizes Huber's original result \cite[Ann. Math., 1954]Huber and may be regarded as a sharp counterpart of Y. Wang's isoperimetric inequality in the unit ball \cite[Adv. Math., 2015]Wang.