Nodal geometry, heat diffusion and Brownian motion

DOI10.2140/apde.2018.11.133zbMath1378.35208arXiv1602.07110OpenAlexW3100647802MaRDI QIDQ2409089

Mayukh Mukherjee, Bogdan Georgiev

Publication date: 10 October 2017

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.07110

zbMATH Keywords

Brownian motionnodal domainsLaplace eigenfunctions

Mathematics Subject Classification ID

Heat equation (35K05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Applications of differential geometry to physics (53Z05) Local Riemannian geometry (53B20)

Related Items

Some applications of heat flow to Laplace eigenfunctions ⋮ Nodal sets of Laplace eigenfunctions under small perturbations ⋮ Some remarks on nodal geometry in the smooth setting ⋮ On the diffusion geometry of graph Laplacians and applications ⋮ On the lower bound of the inner radius of nodal domains ⋮ A pointwise inequality for derivatives of solutions of the heat equation in bounded domains ⋮ Wasserstein distance, Fourier series and applications ⋮ On maximizing the fundamental frequency of the complement of an obstacle ⋮ Density of zero sets for sums of eigenfunctions ⋮ Inner radius of nodal domains of quantum ergodic eigenfunctions ⋮ Faber-Krahn type inequalities and uniqueness of positive solutions on metric measure spaces ⋮ Towards optimal gradient bounds for the torsion function in the plane ⋮ Localisation of the first eigenfunction of a convex domain

Cites Work

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• On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold
• Some bounds for principal frequency
• The size of the first eigenfunction of a convex planar domain
• Sign and area in nodal geometry of Laplace eigenfunctions
• Sobolev Spaces
• Brownian Motion

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