Abstract We devise some differential forms after Chern to compute a family of formulas for comparing total mean curvatures of nested hypersurfaces in Riemannian manifolds. This yields a quicker proof of a recent result of the author with Joel Spruck, which had been obtained via Reilly’s identities.

Mohammad Ghomi

Advanced Nonlinear Studies

高级非线性研究旨在发表关于非线性问题的论文，特别是那些涉及微分方程、动力系统和相关领域的论文。它还将发布这些领域在工程和科学问题上的新颖有趣的应用。提交给本刊的论文必须包含原创、及时和重要的成果。文章通常（但并非总是）按照收到最终副本时的顺序发表。

The journal "Advanced Nonlinear Studies" aims to publish research papers on nonlinear problems, particularly those involving differential equations, dynamical systems, and related fields. It will also feature novel and interesting applications of these areas in engineering and scientific issues. Submitted papers must contain original, timely, and significant findings. Articles are typically published in the order in which the final versions are received, although this is not always the case.

《Advanced Nonlinear Studies》期刊致力于发表关于非线性问题的研究论文，特别是涉及微分方程、动力系统及相关领域的研究。期刊还将发布这些领域在工程和科学问题上的新颖和有趣的应用。提交给本刊的论文必须包含原创性、时效性和重要性的研究成果。文章通常（但并非总是）按照收到最终稿件的顺序发表。

Category	Quartile
数学	2
数学, 数学	2
数学, 应用数学	2

Comparison formulas for total mean curvatures of Riemannian hypersurfaces

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Category	Quartile
MATHEMATICS, APPLIED	1