- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 Some results of evolution of the first eigenvalue of weighted $p$-Laplacian along the extended Ricci flow Commun. Korean Math. Soc. 2020 Vol. 35, No. 3, 953-966 https://doi.org/10.4134/CKMS.c190353Published online July 5, 2020 Shahroud Azami Imam Khomeini International University Abstract : In this article we study the evolution and monotonicity of the first non-zero eigenvalue of weighted $p$-Laplacian operator which it acting on the space of functions on closed oriented Riemannian $n$-manifolds along the extended Ricci flow and normalized extended Ricci flow. We show that the first eigenvalue of weighted $p$-Laplacian operator diverges as $t$ approaches to maximal existence time. Also, we obtain evolution formulas of the first eigenvalue of weighted $p$-Laplacian operator along the normalized extended Ricci flow and using it we find some monotone quantities along the normalized extended Ricci flow under the certain geometric conditions. Keywords : Laplace, extended Ricci flow, eigenvalue MSC numbers : 58C40, 53C44, 53C21 Downloads: Full-text PDF   Full-text HTML

 Copyright © Korean Mathematical Society. All Rights Reserved. The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd