论文标题
Coarea不平等
The Coarea Inequality
论文作者
论文摘要
本文的目的是提供一个独立的证据，证明了Coarea不平等的一般情况，也称为Eilenberg不平等。结果是已知的，但我们不知道任何地方都会写所有细节的证明。已知的证明是基于戴维斯的困难结果。我们的证明是基本的，不使用戴维斯定理。取而代之的是，我们使用了一个优雅的论点，我们通过Mathoverflow从Nazarov学到了这一点。我们还获得了Coarea不平等的一些概括。
The aim of this paper is to provide a self-contained proof of a general case of the coarea inequality, also known as the Eilenberg inequality. The result is known, but we are not aware of any place that a proof would be written with all details. The known proof is based on a difficult result of Davies. Our proof is elementary and does not use Davies' theorem. Instead we use an elegant argument that we learned from Nazarov through MathOverflow. We also obtain some generalizations of the coarea inequality.
