Displaying similar documents to “Harmonic maps and the topology of manifolds with positive spectrum and stable minimal hypersurfaces.”

Asphericity of symmetric presentations

Fulvia Spaggiari (2006)

Publicacions Matemàtiques

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Using the notion of relative presentation due to Bogley and Pride, we give a new proof of a theorem of Prishchepov on the asphericity of certain symmetric presentations of groups. Then we obtain further results and applications to topology of low-dimensional manifolds.

Divergence forms of the infinity-Laplacian.

Luigi D'Onofrio, Flavia Giannetti, Tadeusz Iwaniec, Juan Manfredi, Teresa Radice (2006)

Publicacions Matemàtiques

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The central theme running through our investigation is the infinity-Laplacian operator in the plane. Upon multiplication by a suitable function we express it in divergence form, this allows us to speak of weak infinity-harmonic function in W1,2. To every infinity-harmonic function u we associate its conjugate function v. We focus our attention to the first order Beltrami type equation for h= u + iv

Remarks on subharmonic envelopes.

Duong Ngoc Son (2006)

Publicacions Matemàtiques

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We prove that the subharmonic envelope of a lower semicontinuous function on Omega is harmonic on a certain open subset of Omega, using a very classical method in potential theory. The result gives simple proofs of theorems on harmonic measures and Jensen measures obtained by Cole and Ransford.

Selections generating new topologies.

Valentin Gutev, Artur Tomita (2007)

Publicacions Matemàtiques

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Every (continuous) selection for the non-empty 2-point subsets of a space X naturally defines an interval-like topology on X. In the present paper, we demonstrate that, for a second-countable zero-dimensional space X, this topology may fail to be first-countable at some (or, even any) point of X. This settles some problems stated in [7].