EVALUATION OF A CLASS OF THE LAPLACE OPERATOR DETERMINANTS CONNECTED WITH QUANTUM GEOMETRY OF p-BRANES

1991 ◽  
Vol 06 (08) ◽  
pp. 669-675 ◽  
Author(s):  
A.A. BYTSENKO ◽  
YU. P. GONCHAROV
Keyword(s):  
Laplace Operator ◽  
Trace Formula ◽  
Real Line ◽  
Line Bundles ◽  
Riemannian Surface ◽  
Quantum Geometry ◽  
Selberg Trace Formula ◽  
Riemannian Surfaces ◽  
Determinants Of Laplacians ◽  
The Laplace Operator

We evaluate the determinants of Laplacians acting in real line bundles over the manifolds Tp−1×H2/Γ, T=S1, H2/Γ is a compact Riemannian surface of genus g>1. Such determinants may be important in building quantum geometry of closed p-branes. The evaluation is based on the Selberg trace formula for compact Riemannian surfaces.

scholarly journals An upper bound for λ1 for Γ(q) and Γ0(q)

1990 ◽  
Vol 33 (2) ◽  
pp. 241-250
Author(s):  
C. J. Mozzochi
Keyword(s):  
Discrete Spectrum ◽  
Laplace Operator ◽  
Trace Formula ◽  
Positive Constant ◽  
Upper Bound ◽  
Selberg Trace Formula ◽  
Absolute Positive Constant ◽  
Image Position ◽  
The Laplace Operator

Under the assumption of the Selberg conjecture I establish by means of the Selberg trace formula the following:Theorem. Let Γ denote Γ(q) or Γ0(q), q square-free. Let Δq denote the Laplace operator on L2(Γ\H), and let Σq denote its discrete spectrum. Then there exists an absolute positive constant A such that for q≧A

scholarly journals Selberg's trace formula on thek-regular tree and applications

2003 ◽  
Vol 2003 (8) ◽  
pp. 501-526 ◽  
Author(s):  
Audrey Terras ◽  
Dorothy Wallace
Keyword(s):  
Asymptotic Formula ◽  
Zeta Function ◽  
Trace Formula ◽  
Geodesic Flow ◽  
Prime Number Theorem ◽  
Selberg Trace Formula ◽  
Regular Tree ◽  
Graph Theoretic ◽  
Upper Half Plane ◽  
The Laplace Operator

We survey graph theoretic analogues of the Selberg trace and pretrace formulas along with some applications. This paper includes a review of the basic geometry of ak-regular treeΞ(symmetry group, geodesics, horocycles, and the analogue of the Laplace operator). A detailed discussion of the spherical functions is given. The spherical and horocycle transforms are considered (along with three basic examples, which may be viewed as a short table of these transforms). Two versions of the pretrace formula for a finite connectedk-regular graphX≅Γ\Ξare given along with two applications. The first application is to obtain an asymptotic formula for the number of closed paths of lengthrinX(without backtracking but possibly with tails). The second application is to deduce the chaotic properties of the induced geodesic flow onX(which is analogous to a result of Wallace for a compact quotient of the Poincaré upper half plane). Finally, the Selberg trace formula is deduced and applied to the Ihara zeta function ofX, leading to a graph theoretic analogue of the prime number theorem.

scholarly journals Properties of the resolvent of the Laplace operator on a two-dimensional sphere and a trace formula

2016 ◽  
Vol 8 (3) ◽  
pp. 22-40 ◽  
Author(s):  
Arsen Il'gizovich Atnagulov ◽  
Victor Antonovich Sadovnichii ◽  
Ziganur Yusupovich Fazullin
Keyword(s):  
Laplace Operator ◽  
Trace Formula ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
The Laplace Operator

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 A Selberg trace formula for hypercomplex analytic cusp forms

2015 ◽  
Vol 148 ◽  
pp. 398-428 ◽  
Author(s):  
D. Grob ◽  
R.S. Kraußhar
Keyword(s):  
Trace Formula ◽  
Cusp Forms ◽  
Selberg Trace Formula
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