In dimension d ≥ 5, we consider the differential operator (1.1) H0 = −∆+ τζ(x)|x|(−∆θ), ε > 0, τ > 0, where ∆θ is the Laplace-Beltrami operator on the unit sphere S = {x ∈ R : |x| = 1} and ζ is the characteristic function of the complement to the unit ball {x ∈ R : |x| ≤ 1}. The standard argument with separation of variables allows one to define this operator as the orthogonal sum of one-dimens...

In this paper, the generalized helical hypersurfaces x=x(u,v,w) with a time-like axis in Minkowski spacetime E14 are considered. The first and second fundamental form matrices, Gauss map, shape operator matrix of x calculated. Moreover, curvatures hypersurface obtained by using Cayley–Hamilton theorem. umbilical conditions for given. Finally, Laplace–Beltrami is presented E14.

We study the covariant derivatives of an eigenfunction for Laplace–Beltrami operator on a complete, connected Riemannian manifold with nonzero constant sectional curvature. show that along every parallel tensor, derivative is scalar multiple eigenfunction. also polynomial depending eigenvalue and prove some properties. A conjecture motivated by vertex algebraic structure space forms announced, ...

We investigate a large class of elliptic differential inclusions on non-compact complete Riemannian manifolds which involves the Laplace–Beltrami operator and Hardy-type singular term. Depending behavior nonlinear term curvature manifold, we guarantee non-existence existence/multiplicity solutions for studied inclusion. The proofs are based nonsmooth variational analysis as well isometric actio...

The heat coefficients related to the Laplace-Beltrami operator defined on the hyperbolic compact manifold H3/Γ are evaluated in the case in which the discrete group Γ contains elliptic and hyperbolic elements. It is shown that while hyperbolic elements give only exponentially vanishing corrections to the trace of the heat kernel, elliptic elements modify all coefficients of the asymptotic expan...