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On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator W k : = Δ + k x n x n on n is proved. In this note there is shown that in the cases k 0 , k 2 no other transforms of this kind exist and for case k = 2 , all such transforms are described.

On pseudospheres that are quasispheres.

John L. Lewis, Andrew Vogel (2001)

Revista Matemática Iberoamericana

We construct bounded domains D not equal to a ball in n ≥ 3 dimensional Euclidean space, Rn, for which ∂D is homeomorphic to a sphere under a quasiconformal mapping of Rn and such that n - 1 dimensional Hausdorff measure equals harmonic measure on ∂D.

On separately subharmonic functions (Lelong’s problem)

A. Sadullaev (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

The main result of the present paper is : every separately-subharmonic function u ( x , y ) , which is harmonic in y , can be represented locally as a sum two functions, u = u * + U , where U is subharmonic and u * is harmonic in y , subharmonic in x and harmonic in ( x , y ) outside of some nowhere dense set S .

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