Harmonic functions on manifolds of negative curvature

1986 ◽  
Vol 40 (6) ◽  
pp. 915-917 ◽  
Author(s):  
A. G. Losev
2020 ◽  
Vol 64 (10) ◽  
pp. 9-19
Author(s):  
V. V. Volchkov ◽  
Vit. V. Volchkov

2005 ◽  
Vol 11 (4) ◽  
pp. 517-525
Author(s):  
Juris Steprāns

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.


1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.


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