Analytical, geometrical and topological aspects of a class of mean field equations on surfaces

Gabriella Tarantello

doi:10.3934/dcds.2010.28.931

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2010, Volume 28, Issue 3: 931-973. Doi: 10.3934/dcds.2010.28.931

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Analytical, geometrical and topological aspects of a class of mean field equations on surfaces

Gabriella Tarantello^1,

1.
Universitá degli Studi di Roma "Tor Vergata”, Dipartimento di Matematica, Via della Ricerca Scientifica, Roma

Received: February 28, 2010

Revised: March 31, 2010

Published: August 2010

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Abstract

We present some recent results on mean field equations of Liouville type over a closed surface, in presence of Dirac distributions supported at the so called "vortex points". We discuss possible existence and non-existence results as well as uniqueness and multiplicity issues according to the topological and geometrical properties of the surface.

Keywords:

Mean field equations of Liouville type with singular sources,
surfaces with conical singularies,
electroweak vortices.

Mathematics Subject Classification: 53C21, 58J05, 35J60, 35J0, 35J05.

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