[CvGmt News] Seminario di C. Gui (26/7/2016)
Alfonso Sorrentino
sorrentino at mat.uniroma2.it
Wed Jul 20 14:46:33 CEST 2016
SEMINARIO DI ANALISI ED EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Università degli Studi di Roma "Tor Vergata"
Martedi' 26 Luglio 2016, ore 14:30 Aula dal Passo
Speaker: Changfeng Gui (The University of Texas at San Antonio)
Title: The Sphere Covering Inequality and its application to a
Moser-Trudinger type inequality and mean field equations
Abstract:
In this talk, I will present a new inequality: the Sphere Covering
Inequality, which states that the total area of two {\it distinct}
surfaces with Gaussian curvature 1, which are also conformal to the
Euclidean unit disk with the same conformal factor on the boundary, must
be at least $4 \pi$. In other words, the areas of these surfaces must
cover the whole unit sphere after a proper rearrangement. We apply the
Sphere Covering Inequality to show the best constant of a Moser-Trudinger
type inequality conjectured by A. Chang and P. Yang. Other applications of
this inequality include the classification of certain Onsager vortices on
the sphere, the radially symmetry of solutions to Gaussian curvature
equation on the plane, classification of solutions for mean field
equations on flat tori and the standard sphere, etc. The resolution of
several interesting problems in these areas will be presented. The work
is jointly done with Amir Moradifam from UC Riverside.
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