arXiv research

Study critical points of Laplace eigenfunctions in polygons.

Study bounds the measure of zero sets of Neumann Laplace eigenfunctions.

Study small perturbations on low energy Laplace eigenfunctions.

The study uses heat flow to analyze properties of Laplace eigenfunctions on manifolds and domains.

Study finds average number of common zeros for eigenfunctions on a compact manifold.

New upper bound found for nodal sets of Laplace eigenfunctions.

The study bounds quantum eigenfunctions on complex manifolds.

Review of Yau's conjecture on zero sets of Laplace eigenfunctions.

Study of loops in sums of Laplace eigenfunctions on surfaces.

The paper bounds Cheeger ratios of eigenfunctions and their level sets.

New method for minimal submanifolds in spheres using eigenfunctions.

The study improves estimates of zero sets of Laplace eigenfunctions in 2D and 3D.

Geometrically connects Laplace eigenfunctions to Borel-Weil theory on symmetric spaces.

Eigenfunctions of Laplacian form knots in 3-manifolds.

Study heat profiles and eigenfunctions using Brownian motion.

Study on hyperbolic manifolds finds measures of Laplace eigenfunctions restricted to cosphere bundles.

Eigenfunction value distribution shows unimodal density with maximum at zero.

The study bounds the Hausdorff measure of nodal sets of Laplace eigenfunctions.

Proves Nadirashvili's conjecture and Yau's lower bound for Laplace eigenfunctions.

The study sharpens local Bernstein estimates for Laplace eigenfunctions on compact manifolds.

Study geodesics and nodal sets on hyperbolic surfaces, proving finiteness results.

The paper proves inequalities linking Wasserstein distances and eigenfunctions in RCD(K,∞) spaces.

Eigenfunctions on manifolds concentrate near nodal sets.

Generalizes crystallographic properties to all dimensions.

We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.

Improved Kuznecov remainder estimates for generic metrics.

The study proves constant-curvature analogues of hot spots conjecture for triangles.

A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean space. As an application we give a new proof of a result of Burq-Lebeau and othe…

Sharp bounds for eigenfunctions on product spaces restricted to submanifolds.

In this article we examine the concentration and oscillation effects developed by high-frequency eigenfunctions of the Laplace operator in a compact Riemannian manifold. More precisely, we are interested in the structure of the possible invariant semiclassical measures obtained as limits of Wigner measures correspondin…

We prove pointwise bounds for $L^2$ eigenfunctions of the Laplace-Beltrami operator on locally symmetric spaces with $\mathbb{Q}$-rank one if the corresponding eigenvalues lie below the continuous part of the $L^2$ spectrum. Furthermore, we use these bounds in order to obtain some results concerning the $L^p$ spectrum.

Eigenfunctions of collapsing Einstein manifolds are almost constant along fibers.

Infinite volume requires no atoms at the bottom of the spectrum for certain groups.

The study finds conditions for minimal spheres into ellipsoids using eigenfunctions.

It is proved that if a Paley-Wiener family of eigenfunctions of the Laplace operator in $\mathbb R^3$ vanishes on a real analytically ruled two-dimensional surface $S \subset \mathbb R^3$ then $S$ is a union of cones, each of which is contained in a translate of the zero set of a nonzero harmonic homogeneous polynomial…

The study finds multiple maxima for eigenfunctions on positively curved spheres.

The study examines eigenfunctions on lens spaces using harmonic-counting measures.

The paper bounds eigenvalues and integrals of eigenfunctions on hyperbolic manifolds.

Study covariant derivatives of eigenfunctions on curved spaces, proving they are scalar multiples of the functions.

Spectral calculus simplifies manifold learning with eigenfunctions.

Study on variance of Laplace eigenfunctions on manifolds.

Self-focal points on ellipsoids of dimension 3 or higher are rare.

Estimates average number of common zeros of Laplacian eigenfunctions on manifolds.

This purpose of this write-up is to share an idea for accurate computation of Laplace eigenvalues on a broad class of smooth domains. We represent the eigenfunction $u$ as a linear combination of eigenfunctions corresponding to the common eigenvalue $ρ^{2}$:\EQN{6}{1}{}{0}{\RD{\CELL{u(r,θ) =\sum_{n=0}^{N}P_{n}J_{n}(ρ) …

New Finslerian Ressiner-Nordstrom spacetime with constant flag curvature.

The study examines surfaces in isotropic space with specific Gauss map properties.

Study meromorphic open-string vertex algebras and modules over Riemannian manifolds.

Study on eigenfunctions on sphere configurations, proving non-existence and construction of critical eigensections.