Related papers: Numerical calculation of the lowest eigenmodes of …
In this paper, we study eigenvalues of the poly-Laplacian with arbitrary order on a bounded domain in an $n$-dimensional Euclidean space and obtain a lower bound for eigenvalues, which gives an important improvement of results due to Levine…
We study the 3D Neuman magnetic Laplacian in the presence of a semi-classical parameter and a non-uniform magnetic field with constant intensity. We determine a sharp two term asymptotics for the lowest eigenvalue, where the second term…
In this paper, we prove the nonexistence of $L^2$ harmonic 1-forms on a complete super stable minimal submanifold $M$ in hyperbolic space under the assumption that the first eigenvalue $\lambda_1 (M)$ for the Laplace operator on $M$ is…
We obtain geometric lower bounds for the low Steklov eigenvalues of finite-volume hyperbolic surfaces with geodesic boundary. The bounds we obtain depend on the length of a shortest multi-geodesic disconnecting the surfaces into connected…
See math.CV/0509030 which replaces this paper.
We derive lower bounds for the essential spectrum of the Hodge-Laplacian on geometrically finite orbifolds and their suborbifolds.
In this paper, we obtain lower bounds for the first eigenvalue to some kinds of the eigenvalue problems for Bi-drifted Laplacian operator on compact manifolds (also called a smooth metric measure space) with boundary and $m$-Bakry-Emery…
We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves,…
We estimate explicit lower bounds for the isoperimetric profiles of the Riemannian product of a compact manifold and the Euclidean space with the flat metric, $(M^m\times \mathbb{R}^n,g+g_E)$, $m,n>1$. In particular, we introduce a lower…
We construct an explicit lower bound for the volume of a complex hyperbolic orbifold that depends only on dimension.
In this paper, we study the shape optimization problem for the first eigenvalue of the $p$-Laplace operator with the mixed Neumann-Dirichlet boundary conditions on multiply-connected domains in hyperbolic space. Precisely, we establish that…
We prove that the deformation space AH(M) of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with incompressible boundary is locally connected at minimally parabolic points. Moreover, spaces of Kleinian…
We obtain sharp lower bounds for the first eigenvalue of four types of eigenvalue problem defined by the bi-Laplace operator on compact manifolds with boundary and determine all the eigenvalues and the corresponding eigenfunctions of a…
We prove lower bound for the first closed or Neumann nonzero eigenvalue of the Laplacian on a compact quaternion-K\"ahler manifold in terms of dimension, diameter, and scalar curvature lower bound. It is derived as large time implication of…
We consider the Laplacian with a non-homogeneous metric in a tubular neighbourhood of a compact hypersurface in the Euclidean space of arbitrary dimension, subject to Neumann boundary conditions. It is shown that, in the limit of the width…
We equip the whole tangent space $TM$ to a hyperbolic manifold $M$ (of constant sectional curvature -1) with a natural metric in an intrinsic way, so that the isometries of $M$ extend to isometries of $TM$ by holomorphic continuation. The…
In this work we introduce a new method for the construction of minimal submanifolds of codimension two in even dimensional spheres and hyperbolic spaces. This is based on the theory of complex-valued harmonic morphisms. This gives the first…
The $n$-dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the $(n+1)$-dimensional complex projective space, which is isometric to the real Grassmann manifold of oriented 2-…
We study eigenvalues and eigenfunctions of the Laplacian on the surfaces of four of the regular polyhedrons: tetrahedron, octahedron, icosahedron and cube. We show two types of eigenfunctions: nonsingular ones that are smooth at vertices,…
The Novikov-Shubin invariants for a non-compact Riemannian manifold M can be defined in terms of the large time decay of the heat operator of the Laplacian on square integrable p-forms on M. For the (2n+1)-dimensional Heisenberg group H,…