 
Summary: Growth of Energy in Minimal Surface Bubbles
John Douglas Moore
Department of Mathematics
University of California
Santa Barbara, CA, USA 93106
email: moore@math.ucsb.edu
Preliminary version
Abstract
This article is concerned with developing tools for investigating har
monic maps f : M from a closed Riemann surface into a compact
manifold M of dimension at least three, using a perturbative approach
based upon the energy of Sacks and Uhlenbeck. We present a replace
ment procedure for harmonic maps which is similar to one that has
been used for harmonic maps, and show how it can be used to investigate
the structure of critical points for the energy, when > 1 is sufficiently
close to one. We give an estimate on the rate of growth of the energy
density in the bubbles of such critical points as 1, when the bubbles
are at a distance at least L0 > 0 from the base.
1 Prologue
The Morse theory of geodesics is a highly successful application of global analysis
