The inner radius of nodal domains in high dimensions

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Heat equation (35K05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Cites Work

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Nodal sets for solutions of elliptic equations
Differential Harnack inequalities on Riemannian manifolds. I: Linear heat equation
On the lowest eigenvalue of the Laplacian for the intersection of two domains
On the parabolic kernel of the Schrödinger operator
Nodal sets of eigenfunctions on Riemannian manifolds
Über Knoten von Eigenfunktionen des Laplace-Beltrami-Operators
Harnack inequalities on a manifold with positive or negative Ricci curvature
Heat kernel asymptotics and the distance function in Lipschitz Riemannian manifolds
Hitting probabilities for Brownian motion on Riemannian manifolds.
Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises.
Beweis, daß unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt.
Elliptic partial differential equations of second order
Gaussian upper bounds for the heat kernels of some second-order operators on Riemannian manifolds
Nodal geometry, heat diffusion and Brownian motion
On the lower bound of the inner radius of nodal domains
Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
Can one see the fundamental frequency of a drum?
Inégalités isopérimétriques et applications
On the Inner Radius of a Nodal Domain
Local Asymmetry and the Inner Radius of Nodal Domains
Heat Kernel Bounds on Hyperbolic Space and Kleinian Groups
A lower bound for the heat kernel
Off diagonal short time asymptotics for fundamental solution of diffusion equation
Lecture notes on quantitative unique continuation for solutions of second order elliptic equations
An elliptic adaptation of ideas of Carleman and Domar from complex analysis related to Levinson’s loglog theorem
QUANTITATIVE PROPAGATION OF SMALLNESS FOR SOLUTIONS OF ELLIPTIC EQUATIONS

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