scholarly journals Evolution of the First Eigenvalue of a (<i>p</i>,<i>q</i>)-Laplacian Under a Harmonic Ricci Flow

2021 ◽  
Vol 11 (04) ◽  
pp. 205-217
Author(s):  
Paul Bracken
Keyword(s):  
Ricci Flow ◽  
First Eigenvalue ◽  
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

scholarly journals Lichnerowicz-Obata Estimate, Almost Parallel p-form and Almost Product Manifolds

2021 ◽  
Author(s):  
Masayuki Aino
Keyword(s):  
Riemannian Manifolds ◽  
First Eigenvalue ◽  
Type Estimate ◽  
The First Eigenvalue ◽  
Hausdorff Approximation

AbstractWe show a Lichnerowicz-Obata type estimate for the first eigenvalue of the Laplacian of n-dimensional closed Riemannian manifolds with an almost parallel p-form ($$2\le p \le n/2$$ 2 ≤ p ≤ n / 2 ) in $$L^2$$ L 2 -sense, and give a Gromov-Hausdorff approximation to a product $$S^{n-p}\times X$$ S n - p × X under some pinching conditions when $$2\le p<n/2$$ 2 ≤ p < n / 2 .

scholarly journals First eigenvalue of submanifolds in Euclidean space

2000 ◽  
Vol 24 (1) ◽  
pp. 43-48
Author(s):  
Kairen Cai
Keyword(s):  
Euclidean Space ◽  
Fundamental Form ◽  
Second Fundamental Form ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
The Second Fundamental Form ◽  
Compact Submanifold

We give some estimates of the first eigenvalue of the Laplacian for compact and non-compact submanifold immersed in the Euclidean space by using the square length of the second fundamental form of the submanifold merely. Then some spherical theorems and a nonimmersibility theorem of Chern and Kuiper type can be obtained.

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