scholarly journals The sharp lower bound of the first Dirichlet eigenvalue for geodesic balls

2021 ◽  
Author(s):  
Haibin Wang ◽  
Guoyi Xu ◽  
Jie Zhou
Keyword(s):  
Lower Bound ◽  
Dirichlet Eigenvalue ◽  
First Dirichlet Eigenvalue ◽  
Sharp Lower Bound

Lower bounds for the first Dirichlet eigenvalue of the Laplacian for domains in hyperbolic space

2015 ◽  
Vol 160 (2) ◽  
pp. 191-208 ◽  
Author(s):  
SERGEI ARTAMOSHIN
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Negative Curvature ◽  
Connected Space ◽  
Constant Negative Curvature ◽  
Dirichlet Eigenvalue ◽  
Dirichlet Eigenvalues ◽  
First Dirichlet Eigenvalue ◽  
A New Technique ◽  
Simply Connected

AbstractWe consider domains in a simply connected space of constant negative curvature and develop a new technique that improves existing classical lower bound for Dirichlet eigenvalues obtained by H. P. McKean as well as the lower bounds recently obtained by A. Savo.

scholarly journals A new proof of the bound for the first Dirichlet eigenvalue of the Laplacian operator

2014 ◽  
Vol 22 (2) ◽  
pp. 129-140
Author(s):  
Chang-Jun Li ◽  
Xiang Gao
Keyword(s):  
Lower Bound ◽  
Heat Equation ◽  
Ricci Curvature ◽  
Gradient Estimate ◽  
Laplacian Operator ◽  
Dirichlet Eigenvalue ◽  
First Dirichlet Eigenvalue

AbstractIn this paper, we present a new proof of the upper and lower bound estimates for the first Dirichlet eigenvalue $\lambda _1^D \left({B\left({p,r} \right)} \right)$ of Laplacian operator for the manifold with Ricci curvature Rc ≥ −K, by using Li-Yau’s gradient estimate for the heat equation.

scholarly journals A comparison theorem for the first Dirichlet eigenvalue of a domain in a Kaehler submanifold

1994 ◽  
Vol 56 (2) ◽  
pp. 267-277
Author(s):  
Francisco J. Carreras ◽  
Fernando Giménez ◽  
Vicente Miquel
Keyword(s):  
Outer Radius ◽  
Holomorphic Sectional Curvature ◽  
First Eigenvalue ◽  
Kaehler Manifold ◽  
Dirichlet Eigenvalue ◽  
Totally Geodesic Submanifold ◽  
The First Eigenvalue ◽  
First Dirichlet Eigenvalue ◽  
Dirichlet Eigenvalue Problem ◽  
Sharp Lower Bound

AbstractWe give a sharp lower bound for the first eigenvalue of the Dirichlet eigenvalue problem on a domain of a complex submanifold of a Kaehler manifold with curvature bounded from above. The bound on the first eigenvalue is given as a function of the extrinsic outer radius and the bounds on the curvature, and it is attained only on geodesic spheres of a space of constant holomorphic sectional curvature embedded in the Kaehler manifold as a totally geodesic submanifold.

scholarly journals A LOWER BOUND OF THE FIRST DIRICHLET EIGENVALUE OF A COMPACT MANIFOLD WITH POSITIVE RICCI CURVATURE

2006 ◽  
Vol 17 (05) ◽  
pp. 605-617 ◽  
Author(s):  
JUN LING
Keyword(s):  
Lower Bound ◽  
Ricci Curvature ◽  
Compact Manifold ◽  
Positive Ricci Curvature ◽  
Dirichlet Eigenvalue ◽  
First Dirichlet Eigenvalue

We give a lower bound for the first Dirichlet eigenvalue for a compact manifold with positive Ricci curvature in terms of the lower bound of the Ricci curvature and the interior radius. The result sharpens earlier estimates.

The least distance between extremums and minimal period of solutions to autonomous vector differential equations

2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Lipschitz Constant ◽  
Minimal Period ◽  
Arbitrary Vector ◽  
Vector Norm ◽  
Sharp Lower Bound

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.

scholarly journals Compactness and Sharp Lower Bound for a 2D Smectics Model

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Michael Novack ◽  
Xiaodong Yan
Keyword(s):  
Lower Bound ◽  
Sharp Lower Bound

Success probabilities for second guessers

1980 ◽  
Vol 17 (04) ◽  
pp. 1133-1137 ◽  
Author(s):  
A. O. Pittenger
Keyword(s):  
Lower Bound ◽  
Dimensional Space ◽  
Success Probability ◽  
First Person ◽  
True Location ◽  
Rotationally Symmetric ◽  
The One ◽  
Sharp Lower Bound

Two people independently and with the same distribution guess the location of an unseen object in n-dimensional space, and the one whose guess is closer to the unseen object is declared the winner. The first person announces his guess, but the second modifies his unspoken idea by moving his guess in the direction of the first guess and as close to it as possible. It is shown that if the distribution of guesses is rotationally symmetric about the true location of the unseen object, ¾ is the sharp lower bound for the success probability of the second guesser. If the distribution is fixed and the dimension increases, then for a certain class of distributions, the success probability approaches 1.

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