Nodal sets and horizontal singular sets of ℍ-harmonic functions on the Heisenberg group

DOI10.1142/S0219199713500491zbMath1307.35309MaRDI QIDQ2876621

Long Tian, Xiao-Ping Yang

Publication date: 19 August 2014

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

frequencyHeisenberg groupsub-Laplaciannodal set\(\mathbb{H}\)-harmonic functioncountably rectifiablehorizontal singular set

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Analysis on real and complex Lie groups (22E30) Nilpotent and solvable Lie groups (22E25) Hypoelliptic equations (35H10) Sub-Riemannian geometry (53C17) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (5)

The homogeneous polynomial solutions for the Grushin operator ⋮ Measure upper bounds of nodal sets of Robin eigenfunctions ⋮ The minimum numbers of nodal domains of spherical Grushin-harmonics ⋮ The growth of \(H\)-harmonic functions on the Heisenberg group ⋮ Critical points and level sets of Grushin-harmonic functions in the plane

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