Monotonicity formulas for the first eigenvalue of the weighted p-Laplacian under the Ricci-harmonic flow

被引：10

作者：

Abolarinwa, Abimbola ^{[1
]}

Adebimpe, Olukayode ^{[1
]}

Bakare, Emmanuel A. ^{[2
]}

机构：

[1] Landmark Univ, Dept Phys Sci, Omu Aran, Nigeria

[2] Fed Univ Oye, Dept Math, Nigeria, Oye Ekiti, Nigeria

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2019年 / 2019卷 / 1期

关键词：

Ricci harmonic flow; Laplace-Beltrami operator; Eigenvalue; Monotonicity; Ricci solitons; GEOMETRIC OPERATORS; EVOLUTION;

D O I：

10.1186/s13660-019-1961-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let p,phi be the weighted p-Laplacian defined on a smooth metric measure space. We study the evolution and monotonicity formulas for the first eigenvalue, 1=(p,phi), of p,phi under the Ricci-harmonic flow. We derive some monotonic quantities involving the first eigenvalue, and as a consequence, this shows that 1 is monotonically nondecreasing and almost everywhere differentiable along the flow existence.

引用

页数：16

共 26 条

[1]

Abolarinwa A., 2016, ARXIV160501882MATHDG

[2]

Abolarinwa A., SPECTRUM WEIGH UNPUB

[3] Eigenvalues of the weighted Laplacian under the extended Ricci flow [J].