scholarly journals Heat kernel coefficients of the Laplace operator on the D-dimensional ball

1996 ◽  
Vol 37 (2) ◽  
pp. 895 ◽  
Author(s):  
M. Bordag ◽  
E. Elizalde ◽  
K. Kirsten
Keyword(s):  
Heat Kernel ◽  
Laplace Operator ◽  
Dimensional Ball ◽  
The Laplace Operator

scholarly journals Zeta function determinant of the Laplace operator on theD-dimensional ball

1996 ◽  
Vol 179 (1) ◽  
pp. 215-234 ◽  
Author(s):  
M. Bordag ◽  
B. Geyer ◽  
K. Kirsten ◽  
E. Elizalde
Keyword(s):  
Zeta Function ◽  
Laplace Operator ◽  
Dimensional Ball ◽  
The Laplace Operator

scholarly journals Sharp constants in higher-order heat kernel bounds

2000 ◽  
Vol 61 (2) ◽  
pp. 189-200 ◽  
Author(s):  
Nick Dungey
Keyword(s):  
Heat Kernel ◽  
Laplace Operator ◽  
Adjoint Operator ◽  
Higher Order ◽  
Sharp Constants ◽  
Polynomial Type ◽  
Gaussian Bounds ◽  
Precise Constant ◽  
Kernel Bounds ◽  
The Laplace Operator

We consider a space X of polynomial type and a self-adjoint operator on L2(X) which is assumed to have a heat kernel satisfying second-order Gaussian bounds. We prove that any power of the operator has a heat kernel satisfying Gaussian bounds with a precise constant in the Gaussian. This constant was previously identified by Barbatis and Davies in the case of powers of the Laplace operator on RN. In this case we prove slightly sharper bounds and show that the above-mentioned constant is optimal.

scholarly journals Evolution of the first eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow

2020 ◽  
Vol 18 (1) ◽  
pp. 1518-1530
Author(s):  
Xuesen Qi ◽  
Ximin Liu
Keyword(s):  
Laplace Operator ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Second Fundamental Form ◽  
Coefficient Function ◽  
First Eigenvalue ◽  
Initial Hypersurface ◽  
The Mean ◽  
The Laplace Operator

Abstract In this paper, we discuss the monotonicity of the first nonzero eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow (MCF). By imposing conditions associated with the mean curvature of the initial hypersurface and the coefficient function of the forcing term of a forced MCF, and some special pinching conditions on the second fundamental form of the initial hypersurface, we prove that the first nonzero closed eigenvalues of the Laplace operator and the p-Laplace operator are monotonic under the forced MCF, respectively, which partially generalize Mao and Zhao’s work. Moreover, we give an example to specify applications of conclusions obtained above.

scholarly journals Classification of Some Special Types Ruled Surfaces in Simply Isotropic 3-Space

2017 ◽  
Vol 55 (1) ◽  
pp. 87-98 ◽  
Author(s):  
Murat Kemal Karacan ◽  
Dae Won Yoon ◽  
Nural Yuksel
Keyword(s):  
Real Number ◽  
Laplace Operator ◽  
Fundamental Form ◽  
Three Dimensional ◽  
Ruled Surfaces ◽  
Isotropic Space ◽  
Simply Isotropic Space ◽  
The Laplace Operator ◽  
First Fundamental Form

AbstractIn this paper, we classify two types ruled surfaces in the three dimensional simply isotropic space I13under the condition ∆xi= λixiwhere ∆ is the Laplace operator with respect to the first fundamental form and λ is a real number. We also give explicit forms of these surfaces.

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