 
Summary: Energy Growth in Minimal Surface Bubbles
John Douglas Moore
Department of Mathematics
University of California
Santa Barbara, CA, USA 93106
email: moore@math.ucsb.edu
November 16, 2007
Abstract
This article is concerned with conformal harmonic maps f : M
from a closed connected surface into a compact Riemannian manifold M
of dimension at least four, studied via a perturbative approach based upon
the energy of Sacks and Uhlenbeck. It gives an estimate on the rate
of growth of energy density in the bubbles of minimax energy critical
points as 1, when the bubbles are at a distance at least L0 > 0 from
the base. It also describes additional techniques hopefully useful for the
development of a partial Morse theory for closed parametrized minimal
surfaces (or harmonic surfaces) in compact Riemannian manifolds.
1 Introduction
The Morse theory of geodesics in Riemannian manifolds is a highly success
ful application of the techniques of global analysis to calculus of variations for
