Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362111 
Title:  Harmonic maps of spheres and equivariant theory  
Author:  Ratto, Andrea 
ISNI:
0000 0001 3509 0753


Awarding Body:  University of Warwick  
Current Institution:  University of Warwick  
Date of Award:  1987  
Availability of Full Text: 


Abstract:  
In Chapter I we produce many new harmonic maps of spheres by the qualitative study of the pendulum equations for the join and the Hopf construction. In particular, we obtain Corollary 1.7.1. Let Φ1 : Sp > Sr be any harmonic homogeneous polynomial of degree greater or equal than two, and let Φ2 be the identity map id : Sq > Sq. Then the (q+1)suspension of Φ1 is harmonically representable by an equivariant map of the form Φ1 * Φ2 if and only if q=0 ....5. Corollary 1.11.1. Let [f] E ΠSp be a stable class in the image of the stable Jho momorphism Jp :Πp (0) > ΠSp, p >= 6. Then there exists q > p such that [f] can be represented by a harmonic map Φ : Sp+q+1 > Sq+1. In Chapter II we illustrate equivariant theory and study the rendering problems: in particular, we show that the restriction q=o ...5 in Corollary 1.7.1. can be removed provided that the domain is given a suitable riemannian metric; then, for istance, the groups Πn(Sn) = Z can be rendered harmonic for every n. In Chapter III we describe applications of equivariant theory to the study of Dirichlet problems and warped products; and extensions of the theory to spaces with conical singularities.


Supervisor:  Not available  Sponsor:  Not available  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.362111  DOI:  Not available  
Keywords:  QA Mathematics  
Share: 