Evolution of the first eigenvalue of the clamped plate on manifold along the Ricci flow

2019 ◽  
Vol 65 (5) ◽  
pp. 775-784
Author(s):  
Shahroud Azami
Keyword(s):  
Ricci Flow ◽  
First Eigenvalue ◽  
Clamped Plate ◽  
The First Eigenvalue

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.

Estimate and monotonicity of the first eigenvalue under the Ricci flow

2011 ◽  
Vol 354 (2) ◽  
pp. 451-463 ◽  
Author(s):  
Xiaodong Cao ◽  
Songbo Hou ◽  
Jun Ling
Keyword(s):  
Ricci Flow ◽  
First Eigenvalue ◽  
The First Eigenvalue

EIGENVALUE ESTIMATES ON DOMAIN OF THE POLYDISK

2012 ◽  
Vol 23 (01) ◽  
pp. 1250014
Author(s):  
TAO ZHENG ◽  
DAGUANG CHEN ◽  
MIN CAI
Keyword(s):  
Bounded Domain ◽  
First Eigenvalue ◽  
Dirichlet Laplacian ◽  
Clamped Plate ◽  
Eigenvalue Estimates ◽  
The First Eigenvalue ◽  
Universal Inequalities

In this paper, we investigate universal inequalities for eigenvalues of the Dirichlet Laplacian and the clamped plate problem on a bounded domain in an n-dimensional polydisk 𝔻n. Moreover, from the domain monotonicity of the eigenvalue, we can prove that if the first eigenvalue of the Dirichlet Laplacian tends to [Formula: see text] when the domain tends to the polydisk 𝔻n, then all of the eigenvalues tend to [Formula: see text].

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