First Prairie Analysis Seminar

                                                                    October 19-20, 2001 

                                                 Kansas State University - Manhattan, Kansas




 Featured Speaker: 

 Prof. Fang-Hua Lin,  Courant Institute, NYU. 

   "These two lectures will address some analytical and topological issues concerning Sobolev mappings between 
 manifolds.We shall discuss local and global topological obstructions for smooth maps to be strongly dense or to 
 be weakly sequentially dense in Sobolev mapping spaces,and the topology of Sobolev mappings.We shall also 
 outline a generalized varifold theory for Sobolev mappings and their applications in variational problems."

 Invited Speakers: 

 Prof. Robert Hardt, Rice University 

  Size Minimization and Approximating Problems 

(Thierry De Pauw (Orsay) and Robert Hardt (Rice))

"A  k  dimensional rectifiable current is given by an oriented  k 
 dimensional rectifiable set  M  together with a positive integer-valued density function  D  .  The  mass  of the 
 current is then simply the integral of  D  over  M  (with respect to  k  dimensional Hausdorff measure).  In 1960 
 Federer and Fleming proved the existence of a rectifiable current of least mass for a given boundary.  For  q  in 
 [0,1] ,   the  q-mass of the current is the integral of  D^q  over  M . 
 The case  q = 0  corresponds to  size , introduced by Almgren as a way of using currents to model soap films. 
 We will discuss the existence of a rectifiable current of least  q-mass for a given boundary.  For that purpose we 
 make use of  scans  which are certain functions arising as limits of slices of rectifiable currents."

 Prof. Yisong Yang , Poltytechnic Unversity and IAS (Princeton):

   Nonlinear Problems in Born-Infeld Theory

   "In 1933, M. Born and L. Infeld developed a geometric theory of electromagnetism to accommodate a finite-energy 
 point electric charge modeling the electron. Recently, this theory has become one of the major focuses of theoretical 
 physicists due to its relevance in superstrings and supermembranes. Mathematically, the Born-Infeld theory presents 
 new challenges to analysts. In this talk, we study the Bernstein problems for minimal surface equations, the existence 
 of static Klein-Gordon waves in arbitrary dimensions, and the existence of cosmic strings, in the framework of the 
 Born-Infeld theory."

 Contributed Speakers and Titles of their talks 

 Abstracts of Contributed talks 




Additional Information

 The Prairie Analysis Seminar is a joint project of the Department of Mathematics of  Kansas State University and the 
 Department of Mathematics of The University of Kansas


 Marianne Korten 
 Estela Gavosto
 Charles Moore
 Rodolfo Torres