Lower bounds for the first eigenvalue of the p-Laplace operator on compact manifolds with nonnegative Ricci curvature

2007 ◽  
Vol 7 (1) ◽  
Author(s):  
Huichun Zhang
Keyword(s):  
Laplace Operator ◽  
Ricci Curvature ◽  
Lower Bounds ◽  
Compact Manifolds ◽  
First Eigenvalue ◽  
Nonnegative Ricci Curvature ◽  
The First Eigenvalue

scholarly journals Principal frequency of the p-Laplacian and the inradius of Euclidean domains

2015 ◽  
Vol 07 (03) ◽  
pp. 505-511 ◽  
Author(s):  
Guillaume Poliquin
Keyword(s):  
Lower Bound ◽  
Laplace Operator ◽  
Lower Bounds ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Planar Domains ◽  
Principal Frequency ◽  
The Laplace Operator ◽  
Simply Connected ◽  
Euclidean Domains

We study the lower bounds for the principal frequency of the p-Laplacian on N-dimensional Euclidean domains. For p > N, we obtain a lower bound for the first eigenvalue of the p-Laplacian in terms of its inradius, without any assumptions on the topology of the domain. Moreover, we show that a similar lower bound can be obtained if p > N - 1 assuming the boundary is connected. This result can be viewed as a generalization of the classical bounds for the first eigenvalue of the Laplace operator on simply connected planar domains.

scholarly journals First Eigenvalue of p-Laplacian Along The Normalized Ricci Flow on Bianchi Classes

2020 ◽  
Vol 26 (3) ◽  
pp. 380-392
Author(s):  
Mohammad Javad Habibi Vosta Kolaei ◽  
Shahroud Azami
Keyword(s):  
Laplace Operator ◽  
Lower Bounds ◽  
Ricci Flow ◽  
Homogeneous Manifold ◽  
Upper And Lower Bounds ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Normalized Ricci Flow

Consider M as a 3-homogeneous manifold. In this paper, we are going to study the behavior of the first eigenvalue of p-Laplace operator in a case of Bianchi classes along the normalized Ricci flow also we will give some upper and lower bounds for a such eigenvalue.

scholarly journals Lower bounds on Ricci flow invariant curvatures and geometric applications

2015 ◽  
Vol 2015 (703) ◽  
Author(s):  
Thomas Richard
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Lower Bounds ◽  
Ricci Flow ◽  
Nonnegative Curvature ◽  
Curvature Operator ◽  
Nonnegative Ricci Curvature ◽  
Invariant Cones

AbstractWe consider Ricci flow invariant cones 𝒞 in the space of curvature operators lying between the cones “nonnegative Ricci curvature” and “nonnegative curvature operator”. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to the Ricci flow has its curvature operator which satisfies

The first eigenvalue of the Laplace operator

2016 ◽  
Author(s):  
Baltabek E. Kanguzhin ◽  
Dostilek Dauitbek
Keyword(s):  
Laplace Operator ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
The Laplace Operator

Linear approximation of the first eigenvalue on compact manifolds

2002 ◽  
Vol 45 (4) ◽  
pp. 450-461 ◽  
Author(s):  
Mufa Chen ◽  
E. Scacciatelli ◽  
Liang Yao
Keyword(s):  
Linear Approximation ◽  
Compact Manifolds ◽  
First Eigenvalue ◽  
The First Eigenvalue
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