[CvGmt News] Seminario di C. Gui (26/7/2016)

[Alfonso Sorrentino]

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.