论文标题
抽象度量空间中的脸颊问题
The Cheeger problem in abstract measure spaces
论文作者
论文摘要
我们认为非负$σ$ - 最佳度量空间以及适当的功能性$ p $，扮演周边的角色。我们在此框架中介绍了Cheeger问题，并将许多经典结果扩展到Cheeger常数和Cheeger集中的许多经典结果到此设置，需要对配对量度的空间 - 周期性的最小假设。在整个论文中，绝不会要求测量空间是度量的，最多最多，这需要引入适当的Sobolev空间概念，该空间由Coarea公式与给定的周围引起。
We consider non-negative $σ$-finite measure spaces coupled with a proper functional $P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant and on Cheeger sets to this setting, requiring minimal assumptions on the pair measure space-perimeter. Throughout the paper, the measure space will never be asked to be metric, at most topological, and this requires the introduction of a suitable notion of Sobolev spaces, induced by the coarea formula with the given perimeter.
