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

On the Cheeger–Buser Type Inequalities for the p-Laplacian

2012 ◽  
Vol 12 (2) ◽  
Author(s):  
Ana-Maria Matei
Keyword(s):  
Compact Manifolds ◽  
First Eigenvalue ◽  
Cheeger Constant ◽  
The First Eigenvalue ◽  
Isoperimetric Constant ◽  
The Relationship

AbstractWe study the relationship between the first eigenvalue of the p-Laplacian (p > 1) and Cheeger’s isoperimetric constant for families of compact manifolds and graphs with the Cheeger constant converging to zero.

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.

scholarly journals The first eigenvalue of the $$p-$$ p - Laplacian on quantum graphs

2016 ◽  
Vol 6 (4) ◽  
pp. 365-391 ◽  
Author(s):  
Leandro M. Del Pezzo ◽  
Julio D. Rossi
Keyword(s):  
First Eigenvalue ◽  
Quantum Graphs ◽  
The First Eigenvalue
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