Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
THE RADIUS OF VANISHING BUBBLES IN EQUIVARIANT HARMONIC MAP FLOW FROM D 2 TO S 2
 

Summary: THE RADIUS OF VANISHING BUBBLES IN EQUIVARIANT
HARMONIC MAP FLOW FROM D 2 TO S 2
S.B. ANGENENT # , J. HULSHOF + , AND H. MATANO #
Abstract. We derive an upper bound for the radius R(t) of a vanishing bubble in a family of
equivariant maps F t : D 2
# S 2 which evolve by the Harmonic Map Flow. The self­similar ``type 1''
radius would be R(t) = C # T - t. We prove that R(t) = o(T - t).
1. Introduction. Let N n
# R k be a smooth submanifold. The Dirichlet integral
or energy of a map F from the unit disc D 2
# R 2 into N is defined to be
D[F ] = 1
2 # D 2
|#F (x)| 2 .
Extremals of this energy with prescribed boundary values F | #D 2 are called harmonic
maps. Eells and Sampson [4] introduced the gradient flow for D[F ], now called the
harmonic map flow, in which a family of maps F t : D # N evolves according to the
nonlinear heat equation
#F
#t

  

Source: Angenent, Sigurd - Department of Mathematics, University of Wisconsin at Madison

 

Collections: Mathematics