Euclidean triangles have no hot spots

DOI10.4007/annals.2020.191.1.3zbMath1444.35119arXiv1802.01800OpenAlexW3099707737MaRDI QIDQ2287646

Sugata Mondal, Christopher M. Judge

Publication date: 21 January 2020

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.01800

zbMATH Keywords

Laplace operatorhot spots conjectureNeumann eigenfunctions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Related Items (11)

The hot spots conjecture can be false: some numerical examples ⋮ Any three eigenvalues do not determine a triangle ⋮ Critical points of Laplace eigenfunctions on polygons ⋮ Improved upper bounds for the hot spots constant of Lipschitz domains ⋮ An upper bound on the hot spots constant ⋮ Hot spots in convex domains are in the tips (up to an inradius) ⋮ On the hot spots of quantum graphs ⋮ A spectral approach to the shortest path problem ⋮ The two hyperplane conjecture ⋮ Spectral clustering revisited: information hidden in the Fiedler vector ⋮ Erratum to: ``Euclidean triangles have no hot spots

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