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Examples involving the geometric form of level curves of harmonic functions
Author(s) -
Acker A.,
Payne L.
Publication year - 1985
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670070134
Subject(s) - mathematics , maxima and minima , complement (music) , maxima , plane curve , plane (geometry) , mathematical analysis , harmonic , harmonic function , local structure , geometry , pure mathematics , combinatorics , quantum mechanics , physics , art history , gene , phenotype , chemical physics , art , biochemistry , chemistry , complementation , performance art
In the x ‐ y plane, we give, for example, a Jordan curve Γ containing exactly one local maximum and one local minimum in the y ‐direction, such that some level curve of the capacity potential in the exterior complement of Γ has at least n local maxima and n local minima in the y ‐direction, n being any prescribed number.