A Characteristic Eigenfunction for Minimal Hypersurfaces in Space Forms.
A directional compactification of the complex Bloch variety.
A directional compactification of the complex Fermi surface
A discreteness criterion for the spectrum of the Laplace--Beltrami operator on quasimodel manifolds.
A geometric estimate for a periodic Schrödinger operator
We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator with potential given by the curvature of a closed curve.
A local analytic splitting of the holonomy map on flat connections.
A lower bound for ... on manifolds with boundary.
A lower bound for the error term in Weyl’s law for certain Heisenberg manifolds, II
This article is concerned with estimations from below for the remainder term in Weyl’s law for the spectral counting function of certain rational (2ℓ + 1)-dimensional Heisenberg manifolds. Concentrating on the case of odd ℓ, it continues the work done in part I [21] which dealt with even ℓ.
A lower bound for the least eigenvalue of ... + V.
A lower bound on ... for geometrically finite hyperbolic n-manifolds.
A mean-value lemma and applications
We control the gap between the mean value of a function on a submanifold (or a point), and its mean value on any tube around the submanifold (in fact, we give the exact value of the second derivative of the gap). We apply this formula to obtain comparison theorems between eigenvalues of the Laplace-Beltrami operator, and then to compute the first three terms of the asymptotic time-expansion of a heat diffusion process on convex polyhedrons in euclidean spaces of arbitrary dimension. We also write...
A method of symmetrization ; Applications to heat and spectral estimates
A minorization of the first positive eigenvalue of the scalar laplacian on a compact Riemannian manifold [Book]
A new intrinsic curvature invariant for centroaffine hypersurfaces.
A nilpotent Lie algebra and eigenvalue estimates
The aim of this paper is to demonstrate how a fairly simple nilpotent Lie algebra can be used as a tool to study differential operators on with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.
A Note on the First Nonzero Eigenvalue of the Laplacian Acting of P-Forms.
A note on the isoperimetric constant
A reduction method for proving the existence of solutions to elliptic equations involving the -Laplacian.
A Relation Between Growth and the Spectrum of the Laplacian.
A relationship between volume, injectivity radius, and eigenvalues.